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R

Raj 14/11/2016 in

Rajesh replied | 09/12/2016

A circle consisting of all points where two perpendicular tangent lines to the ellipse cross each other.

Ankit replied | 09/12/2016

In geometry, the director circle of an ellipse or hyperbola (also called the orthoptic circle or Fermatâ€“Apollonius circle) is a circle consisting of all points where two perpendicular tangent lines to the ellipse cross each other.

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N

Neha 14/11/2016 in

Sanjeev replied | 04/12/2016

Differential of y/ differential of x.

Manikandan replied | 08/12/2016

For the curve y=f(x) slope of tangent is dy/dx.

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G

Ganesh 14/11/2016 in

Nirmal Bhasu replied | 06/12/2016

The chord which passes through focus is called focal chord.

Sri Veera Bhadraswamy replied | 10/12/2016

The line which passes through the focus is called focal chord.

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P

Praneeth 14/11/2016 in

What do you mean by parabola?

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.

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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A

Ajay 14/11/2016 in

What is the standard equation of parabola?

Ramesh replied | 19/11/2016

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

A

Anurag replied | 20/11/2016

x2/a2-y2/b2=1

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P

Pratik 14/11/2016 in

What is directrix?

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.

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

What do you mean by eccentricity?

Saurabh replied | 02/12/2016

It is a measure of how much the conic section deviates from being circular. In particular, the eccentricity of a circle is zero.

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 â€˜eâ€™.
Value of â€˜eâ€™ 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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M

Melvin 14/11/2016 in

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

S

Srinivas replied | 27/11/2016

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

S

Srinivas replied | 28/11/2016

y=mx+a/m.

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C

Chetana 14/11/2016 in

What is the angle between the two tangents?

Sanjeev replied | 12/12/2016

(m1-m2)/(1+m1m2).
Where m1 and m2 are the slope of the tangents.

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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M

Meenakshi 14/11/2016 in

What is the standard equation of normal?

Rachna replied | 18/11/2016

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

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

What do you mean by polar with respect to parabola?

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.

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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A

Ambar 14/11/2016 in

What are the properties of tangents?

Nagesh replied | 25/11/2016

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

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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S

Sounak 14/11/2016 in

What is the equation of parabola if the focus (-a, 0) and the directrix is x = a?

Sarvajeet replied | 02/12/2016

Square of y = -4ax.

Ankit replied | 09/12/2016

Square of y = -4ax.

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A

Abdul 14/11/2016 in

What is the equation of parabola along y- axis if the focus of the parabola on its positive side and the directrix y = -a?

D Chandra replied | 30/11/2016

x^2= 4ay.

Sarvajeet replied | 02/12/2016

Square of x = 4ay.

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S

Sanjay 14/11/2016 in

What is the equation of parabola if focus (0, -a) and directrix y = a?

Ajay replied | 23/11/2016

Its square of x = - 4 ay. From the given data, square of x + square of (y+a) i.e., distance of any point on parabola from focus = distance of pt. from directrix i.e. square of (y-a). On solving it, you get the given result.

Sarvajeet replied | 24/11/2016

Square of x = -4*a*y.

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V

Vishal 14/11/2016 in

What is latus rectum?

Sarvajeet replied | 26/11/2016

In any conics (i.e., parabola or ellipse or hyperbola ), a line passing through its focus and parallel to its directrix is called the latus rectum.
For example, in parabola: square of y = 4ax, the equation of the latus ractum y=a and its length = 4a;
in ellipse: square of (x/a) + square of (y/b)=1, a>b, the equation of the latus ractum y=ae, -ae and its length = 2(square...  more»
In any conics (i.e., parabola or ellipse or hyperbola ), a line passing through its focus and parallel to its directrix is called the latus rectum.
For example, in parabola: square of y = 4ax, the equation of the latus ractum y=a and its length = 4a;
in ellipse: square of (x/a) + square of (y/b)=1, a>b, the equation of the latus ractum y=ae, -ae and its length = 2(square of b)/a;
in hyperbola: square of (x/a) - square of (y/b)=1, the equation of the latus ractum y=ae, -ae and its length = 2(square of b)/a; «less

Ankit replied | 09/12/2016

In any conics (i.e., parabola or ellipse or hyperbola ), a line passing through its focus and parallel to its directrix is called the latus rectum.
For example, in parabola: square of y = 4ax, the equation of the latus ractum y=a and its length = 4a;
in ellipse: square of (x/a) + square of (y/b)=1, a>b, the equation of the latus ractum y=ae, -ae and its length = 2(square...  more»
In any conics (i.e., parabola or ellipse or hyperbola ), a line passing through its focus and parallel to its directrix is called the latus rectum.
For example, in parabola: square of y = 4ax, the equation of the latus ractum y=a and its length = 4a;
in ellipse: square of (x/a) + square of (y/b)=1, a>b, the equation of the latus ractum y=ae, -ae and its length = 2(square of b)/a;
in hyperbola: square of (x/a) - square of (y/b)=1, the equation of the latus ractum y=ae, -ae and its length = 2(square of b)/a; «less

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U

Uday 14/11/2016 in

What are the terms related to parabola?

Abhilash replied | 02/12/2016

u-shaped curve with certain specific properties. Formally, a parabola is defined as follows:- For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus of points such that the distance to the focus equals the distance to the directrix.

Ankit replied | 09/12/2016

u-shaped curve with certain specific properties. Formally, a parabola is defined as follows:- For a given point, called the focus, and a given line not through the focus, called the directrix, a parabola is the locus of points such that the distance to the focus equals the distance to the directrix.

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J

Jogendra 14/11/2016 in

What is the parametric equation of a chord?

Vanaja replied | 29/11/2016

The chord of contact is a chord formed from joining the points of intersection of the parabola and two tangents emanating from an external point T. Both methods are used to derive the equation of the chord of contact.

Ankit replied | 09/12/2016

The chord of contact is a chord formed from joining the points of intersection of the parabola and two tangents emanating from an external point T. Both methods are used to derive the equation of the chord of contact.

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T

Tashiruddin 14/11/2016 in

What do you mean by curve with respect to parabola?

Abhilash replied | 01/12/2016

A parabola is a curve where any point is at an equal distance from: a fixed point (the focus ) and a fixed straight line (the directrix).

Ankit replied | 09/12/2016

A parabola is a curve where any point is at an equal distance from: a fixed point (the focus ) and a fixed straight line (the directrix).

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S

Shreyansh 14/11/2016 in

What do you mean by conormal point?

Prateek replied | 19/11/2016

The points on the curve at which the normal pass through a common point are called co-normal points.

Sanjeev replied | 12/12/2016

Perpendicular to each other.

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A

Ambar 14/11/2016 in

Find the vertex, axis, focus, directrix, latus rectum of the parabola: (square of y) + 8y + x + 19 = 0?

Sarvajeet replied | 26/11/2016

It's vertex = (-3, -4),
axis y=-4,
focus (-13/4, -4),
Directrix x= -11/4,
the equation of the Latus rectum x=-13/4 and the length of the Latus rectum=1.

Ankit replied | 09/12/2016

It's vertex = (-3, -4),
axis y=-4,
focus (-13/4, -4),
Directrix x= -11/4,
the equation of the Latus rectum x=-13/4 and the length of the Latus rectum=1.

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R

Rayaan 14/11/2016 in

Find the equation of the chord of a parabola with respect to the point (x, y)?

K.v.ratnamala replied | 07/12/2016

y*y=4ax.

Rajneesh replied | 13/12/2016

y*y = 4ax.

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K

Khushboo 14/11/2016 in

Find the equation of tangents to the parabola drawn from an external point P?

K.v.ratnamala replied | 07/12/2016

if (x,y) is the point then y*y - 4ax is the tangent to the parabola.

Manibhushan replied | 07/12/2016

The equation of the parabola is x^2=4ay or y=x^2/(4a) . We are drawing tangent lines through the point (2,-3) to the parabola.
The slopes of the tangent lines are given by the first derivative evaluated at the point of tangency.
y=x^2/(4a)==>y'=x/(2a).
Thus the equation of a tangent line to the parabola at (x,x^2/(4a)) and through point (2,-3) is y+3=x/(2a)(x-2) or y=x^2/(2a)-x/a-3....  more»
The equation of the parabola is x^2=4ay or y=x^2/(4a) . We are drawing tangent lines through the point (2,-3) to the parabola.
The slopes of the tangent lines are given by the first derivative evaluated at the point of tangency.
y=x^2/(4a)==>y'=x/(2a).
Thus the equation of a tangent line to the parabola at (x,x^2/(4a)) and through point (2,-3) is y+3=x/(2a)(x-2) or y=x^2/(2a)-x/a-3. But y=(x^2)/(4a). So,
x^2/(4a)=x^2/(2a)-x/a-3 Multiplying through by 4a we get:
x^2=2x^2-4x-12a or x^2-4x-12a=0 . Using the quadratic formula we get:
x=(4+-sqrt(16-4(1)(-12a)))/(2)
x=(4+-sqrt(16(1+3a)))/2
x=2+-2sqrt(1+3a). «less

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A

Abishiek 14/11/2016 in

Find the equation of the chord of parabola whose midpoint is (x1, y1)?

Sarvajeet replied | 01/12/2016

The equation of the chord of parabola (Let square of y=4ax) whose midpoint is (x1, y1) is:-
y(y1)-4a(x1)= square of (y1)-4a(x1).

Sarvajeet replied | 03/12/2016

The equation of the chord of parabola (Let square of y=4ax) whose midpoint is (x1, y1) is:-
y(y1)-2a(x-x1)= square of (y1)-4a(x1).

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Y

Yashraj 14/11/2016 in

Find the equation of the parabola whose focus is (1, 1) and the tangent at the vertex is x + y = 1?

K.v.ratnamala replied | 07/12/2016

Since it is passing through focus(1,1) x-y+L=0=>1-1+L=0=>L=0.
x-y=0;x+y=1; by solving these 2 equations we get:-x=1/2;y=1/2.

Ankit replied | 09/12/2016

Since it is passing through focus(1,1) x-y+L=0=>1-1+L=0=>L=0.
x-y=0;x+y=1; by solving these 2 equations we get:-x=1/2;y=1/2.

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