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P

Praneeth 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Parabola

What do you mean by parabola?

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Sarvajeet replied | 26/11/2016

For Parabola, square of y = 4ax, the distance of a point P on the parabola from the focus = its distance (that point P on the parabola) from the directrix i.e., The eccentricity e = 1.

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Sri Veera Bhadraswamy replied | 10/12/2016

sp/pm=1 or e=1 where, sp is the distance between focal and any point on the curve and pm is the distance of the point p from directrix.

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Ajay 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Parabola

What is the standard equation of parabola?

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Ramesh replied | 19/11/2016

Second degree parabola equation is Y=a+bx+cx2

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A

Anurag replied | 20/11/2016

x2/a2-y2/b2=1

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Pratik 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Parabola

What is directrix?

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Manibhushan replied | 08/12/2016

A parabola is a locus of points equidistant from a single point, called the focus of the parabola, and a line, called the directrix of the parabola.

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Rama Krishna replied | 08/12/2016

Dear Student,
Directrix means in Geometry is a fixed line used in describing a Curve or Surface.

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S

Sushmita 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Parabola

What do you mean by eccentricity?

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Sarvajeet replied | 04/12/2016

A conic section, or conic is the locus of a point which moves in a plane so that its distance from a fixed
point is in a constant ratio to its perpendicular distance from a fixed straight line and this constant ratio is
called eccentricity denoted by e .
Value of e Types of conics
e = 1 Parabola
0 < e < 1 Ellipse
e > 1 Hyperbola
e = 0 Circle
e...  more»
A conic section, or conic is the locus of a point which moves in a plane so that its distance from a fixed
point is in a constant ratio to its perpendicular distance from a fixed straight line and this constant ratio is
called eccentricity denoted by ā€˜eā€™.
Value of ā€˜eā€™ Types of conics
e = 1 Parabola
0 < e < 1 Ellipse
e > 1 Hyperbola
e = 0 Circle
e = Infinite Pair of straight lines «less

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Prabhat replied | 03 May

In mathematics, the eccentricity , denoted e is a parameter associated with every conic section. It can be thought of as a measure of how much the conic section deviates from being circular.

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Melvin 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Parabola

What is the equation of tangent of slope m to the parabola?

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S

Srinivas replied | 27/11/2016

y^2=4ax => y =mx+c; c=a/m.

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S

Srinivas replied | 28/11/2016

y=mx+a/m.

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C

Chetana 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Parabola

What is the angle between the two tangents?

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Pankaj replied | 13/12/2016

Angle between two tangents having slope m1 and m2 can be calculated as:
tanx = (m1-m2)/(1+m1m2).

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Prabhat replied | 03 May

the angle between two tangents is given by- (m1-m2)/(1+m1m2).

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Meenakshi 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Parabola

What is the standard equation of normal?

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Rachna replied | 18/11/2016

y-y1= - dx/dy (x-x1)

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Eti replied | 18/11/2016

Equation of normal of any curve at point (x1,y1) is (x-x1)+(dy/dx)(x1,y1)(y-y1)=0

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D

Deepashri 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Parabola

What do you mean by polar with respect to parabola?

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Soujanya replied | 07/12/2016

The polar p of a point A(x0, y0), exterior to the parabola y2 = 2px, is the secant through the contact points of the tangents drawn from the point A to the parabola.

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Mayank replied | 07/12/2016

Polar with respect to parabola is the point on the parabola where the graph happens to intersect any axes (depends upon the equation of parabola). If it is symmetric about the y-axis then put y=0 and find x. Polar=(x, 0).

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Ambar 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Parabola

What are the properties of tangents?

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Nagesh replied | 25/11/2016

First derivative of the equation of the curve can give you slope of the tangent at that point.

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Sarvajeet replied | 26/11/2016

For Parabola, square of y = 4ax,
The equation of tangent, y=mx+(a/m), m=gradient, the tangent always touches at one point of the parabola.

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N

Nazia 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Ellipse

What do you mean by ellipse?

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G

Guddu replied | 22/11/2016

Locus of a point such that whose sum of distances from two fixed point is constant.

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Sarvajeet replied | 03/12/2016

(square of (x/a) ) +(square of (y/b) )=1 and a>b
and eccentricity e <1.
It must contain 1 major axes, 1 minor axes.

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S

Saddam 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Ellipse

What are the properties of ellipse?

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Rohit replied | 13/12/2016

Properties 1. Tangents drawn from a common point, outside the curve are equally inclined to the focal points.
Properties 2. A circle containing the foci and a point p on the curve will intersect the minor axis at the points of intersection of the tangent and the normal to the curve from point.

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Rahul replied | 13/12/2016

Property 1:
Tangents drawn from a common point, outside the curve are equally inclined to the focal points.



PROPERTY 2

A circle containing the foci and a point p on the curve will intersect the minor axis at the points of intersection of the tangent and the normal to the curve from point p.





PROPERTY 3

The length...  more»
Property 1:
Tangents drawn from a common point, outside the curve are equally inclined to the focal points.



PROPERTY 2

A circle containing the foci and a point p on the curve will intersect the minor axis at the points of intersection of the tangent and the normal to the curve from point p.





PROPERTY 3

The length of the minor axis of an ellipse can be found by constructing a line perpendicular to the axis from the focal points, where this line intersects the auxiliary circle will give the length of the minor axis.









PROPERTY 4

Conjugate Diameters





Any diameter of the ellipse, as shown here, may be referred to as a conjugate diameter. This example shows the short conjugate diameter, the long conjugate diameter would pass through the centre and be parallel to a tangent to the curve at r and s.









Constructing the Ellipse given the Conjugate Diameter

PROCEDURE

1. Construct the conjugate diameters TU (long) and RS (short).

2. Take a line from R perpendicular to TU of length CU to find point D.

3. Join D to C.

4. Construct a circle of diameter DC.

5. Take a line from R through the centre of the circle and project it on to meet the circle at G.

6. A line from G through C will give the direction of the minor axis.

7. RE = 1/2 the minor axis.

8. A line from E through C will give the direction of the major axis.

9. RG = 1/2 the major axis.

10. You now have the major and minor axis and can construct the curve.

NOTE: The curve passes through points R, S, T and U.








PROPERTY 1

Tangents drawn from a common point, outside the curve are equally inclined to the focal points.




PROPERTY 2

A circle containing the foci and a point p on the curve will intersect the minor axis at the points of intersection of the tangent and the normal to the curve from point p.





PROPERTY 3

The length of the minor axis of an ellipse can be found by constructing a line perpendicular to the axis from the focal points, where this line intersects the auxiliary circle will give the length of the minor axis.









PROPERTY 4

Conjugate Diameters





Any diameter of the ellipse, as shown here, may be referred to as a conjugate diameter. This example shows the short conjugate diameter, the long conjugate diameter would pass through the centre and be parallel to a tangent to the curve at r and s.









Constructing the Ellipse given the Conjugate Diameter

PROCEDURE

1. Construct the conjugate diameters TU (long) and RS (short).

2. Take a line from R perpendicular to TU of length CU to find point D.

3. Join D to C.

4. Construct a circle of diameter DC.

5. Take a line from R through the centre of the circle and project it on to meet the circle at G.

6. A line from G through C will give the direction of the minor axis.

7. RE = 1/2 the minor axis.

8. A line from E through C will give the direction of the major axis.

9. RG = 1/2 the major axis.

10. You now have the major and minor axis and can construct the curve.

NOTE: The curve passes through points R, S, T and U. «less

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A

Aditya 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Ellipse

What are the special cases of ellipse?

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Pankaj replied | 13/12/2016

If you put a=b then equation of ellipse reduces to x^2+y^2=a^2 and it becomes circle that is the special case of ellipse.

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Rajneesh replied | 13/12/2016

When a=b it must be a circle.

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S

Swarnalakshmi 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Ellipse

What is the equation of horizontal ellipse?

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Pro replied | 21/11/2016

Hi Swarna, any ellipse is horizontal (elongated along x-axis) if its semi-major axis is greater than semi-minor axis (a>b) in canonical equation of ellipse i.e. x2/a2 + y2/b2 = 1, if b>a then it looks vertically elongated and a=b it is circle. You can try some experiments with ellipse here http://www.desmos.com/calculator...  more»
Hi Swarna, any ellipse is horizontal (elongated along x-axis) if its semi-major axis is greater than semi-minor axis (a>b) in canonical equation of ellipse i.e. x2/a2 + y2/b2 = 1, if b>a then it looks vertically elongated and a=b it is circle. You can try some experiments with ellipse here http://www.desmos.com/calculator «less

0 0

Eti replied | 21/11/2016

(x^2)/(a^2)+(y^2)/(b^2)=1,where a>b

0 0

Answer

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A

Ajay 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Ellipse

Define vertical ellipse?

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Sarvajeet replied | 26/11/2016

(square of (x/a) ) +(square of (y/b) )=1 and a

0 0
S

Srinivas replied | 28/11/2016

In it the major axis is y-axis its length is 2b and minor axis is x-axis its length is 2a.

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M

Medha 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Ellipse

What do you mean by eccentric angle of a point?

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Prateek replied | 19/11/2016

Is equal to tan[inverse (a*y / b*x)].

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Sagar replied | 21/11/2016

The eccentric angle of a point on an ellipse with semi major axes of length a and semi minor axes of length b is the angle t in the parametrization.
x = acost
(1)
y = bsint,
(2)
i.e., for a point (x,y),
t=tan^(-1)((ay)/(bx)).

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J

Jitender 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Ellipse

Find the length of major and minor axes of the given equation: 4(square of x) + 9(square of y) = 36?

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Sri Veera Bhadraswamy replied | 10/12/2016

6,4 are the lengths of major and minor axes.

0 0
P

Parveen replied | 12/12/2016

(Major axis)^2=9 so major axis is 3 and (minor axis)^2=4. So, min axis is 2.

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S

Sumit 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Hyperbola

Define hyperbola?

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S

Srinivas replied | 28/11/2016

SIMPLY SAY THAT IN ANY CONIC SECTION ECCENTRICITY e>1

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Sarvajeet replied | 03/12/2016

(square of (x/a) ) - (square of (y/b) )=1
and eccentricity e >1.

0 0

Answer

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B

Bala 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Hyperbola

What is the difference between transverse axes and conjugate axes?

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Sarvajeet replied | 03/12/2016

In hyperbola, (square of (x/a) ) - (square of (y/b) )=1
and eccentricity e >1.
Transverse axes y=0 i.e., x axes.
Conjugate axes x=0 i.e., y axes.

0 0

Sarvajeet replied | 03/12/2016

In hyperbola, (square of (x/a) ) - (square of (y/b) )=1
and eccentricity e >1;
Transverse axes y=0 i.e., x axes
Conjugate axes x=0 i.e., y axes.

0 0

Answer

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S

Shishir 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Hyperbola

Define conjugate formula?

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Lakshmi replied | 24/11/2016

A conjugate is a binomial formed by negating the second term of a binomial. The conjugate of x + y is x ? y, where x and y are real numbers.
If y is imaginary, the process is termed complex conjugation: the complex conjugate of a + bi is a ? bi, where a and b are real.

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Sarvajeet replied | 03/12/2016

Two hyperbolas such that the transverse axis of each is the conjugate axis of the other.
For example (square of (x/a) ) - (square of (y/b) )=1 and (square of (x/b) ) - (square of (y/a) )=1.

0 0

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Nayan 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Hyperbola

Define focal distance of a point?

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V

Vinayak Educational Institute replied | 02/12/2016

Focal length is the distance between the center of a convex lens or a concave mirror and the focal point of the lens or mirror the point where parallel rays of light meet, or converge.

0 0

Arvind Kumar replied | 02/12/2016

The distance of any point on the Hyperbola from the focus is called its focal diistance.

0 0

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N

Name 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Hyperbola

What is the equation of hyperbola if the center is (h, k) and the directions of the axes are parallel to the coordinate axes?

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Rama Krishna replied | 09/12/2016

The Equation of Hyperbola is When the center is (h, k) and Whose Transverse and Conjugate axes are 2a and 2b is { Square of (x-h) / Square of (a) } - { Square of (y-k)/ Square of (b) } = 1.

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Piyush Raj replied | 14/12/2016

(x-h)^2 /a^2 - (y-k)^2/b^2 =1
it is called rectangular hyperbola where a=b so the final equation will be x^2 -y^2 = a^2.

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S

Sample 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Hyperbola

What is the normal equation of hyperbola?

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Dilip replied | 06/12/2016

X^2/a^2 - y^2/b^2=1.

0 0

Ravi replied | 14/12/2016

X^2/A^2-Y^2/B^2=1, where a and b can be any number.

0 0

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K

Kumar 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Hyperbola

What are the properties of hyperbola?

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Siva Naga Raju replied | 22/11/2016

Hyperbola is an open ended conic section i.e., the curve continues indefinitely to infinity.
General equation of a Hyperbola: [square of (x/a) - square of (y/b) = constant].

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A

Anjali replied | 23/11/2016

The asymptotes of a hyperbola lie on the points of intersection of circle containing the foci and tangents from the vertices.
The directrix lies on the point of intersection of the auxiliary circle and the asymptotes.

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H

Hemlatakarla 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Hyperbola

What is conjugate lines?

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Ankit replied | 09/12/2016

Definition of conjugate lines. 1 of a conic section : two lines each of which passes through the pole of the other. 2 of a quadric : two lines so arranged that each intersects the polar line of the other.

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Dilip replied | 11/12/2016

Two lines each of which passes through the pole of the other.

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Mohit 14/11/2016 in  Class XI-XII Tuition (PUC), Mathematics(Class XI-XII Tuition (PUC)), Hyperbola

Define conjugate diameter?

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Vidyadhan replied | 13/12/2016

In geometry, two diameters of a conic section are said to be conjugate if each chord parallel to one diameter is bisected by the other diameter. For example, two diameters of a circle are conjugate if and only if they are perpendicular.

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Abhilash replied | 14/12/2016

Diameters of a hyperbola are conjugate when each bisects all chords parallel to the other. In this case both the hyperbola and its conjugate are sources for the chords and diameters.

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