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B

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Pritesh replied | 26/11/2016

Form forms of Standard Parabola are follows:
y^2=4ax ;
y^2=-4ax ;
x^2=4ay ;
x^2=-4ay

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Rama Krishna replied | 09/12/2016

Square of ( x-h) = { 4p * ( y-k) }.

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Lohith replied | 07/12/2016

Use this standard form of equation x2 (x square )/a2 (a square) - y2 (y square)/b2 (b square) = 1.

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Prabha replied | 11/12/2016

If you take standard hyperbola as:
X^2/a^2- y^2/b^2 =1 the consider x^2/a^2 - y^2/b^2 = 0
Which gives (x/a - y/b) (x/a+y/b) = 0
Solve it to get separate equations.

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Vijay replied | 23/11/2016

x2 – y2 = a2.

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Sarvajeet replied | 03/12/2016

Square of x - Square of y = Square of a.

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Prateek replied | 19/11/2016

It is a line such that the distance between the curve and the line approaches zero as they tend to infinity

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Anurag replied | 20/11/2016

Those equation whose point of intersection meet at infinite.

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B

Bhaskar replied | 21/11/2016

y=mx±?(a2m2?b2) where mm refers to the slope of a tangent line.

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Sarvajeet replied | 03/12/2016

Tangent A: y= mx + square root( square of (am) - square of b), where m=the slope of the tangent=dy/dx.
or at (x1, y1), xx1/square of a - yy1/square of b=1.

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Srinivas replied | 26/11/2016

Eccentricity is define as the ratio of the distance of any point on a conic section from a focus to its distance from the corresponding directrix and it is denoted with "e"; e range from 0 to 1; 0 < e <1.

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Mukesh replied | 27/11/2016

A circle has an eccentricity of zero, so the eccentricity shows you how "un-circular" the curve is. Bigger eccentricities are less curved.
At eccentricity = 0 we get a circle
for 0 < eccentricity < 1 we get an ellipse
for eccentricity = 1 we get a parabola
for eccentricity > 1 we get a hyperbola
for infinite eccentricity we get a line.

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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.

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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.

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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.

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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.

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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.

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Arvind Kumar replied | 02/12/2016

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

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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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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.

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Ravi replied | 14/12/2016

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

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

What do you mean by rectangular hyperbola?

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Sarvajeet replied | 03/12/2016

square of x - square of y= square of a.

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Sri Veera Bhadraswamy replied | 10/12/2016

xy=c^2 is a rectangular hyperbola.

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

What is the director circle of hyperbola?

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Dilip replied | 06/12/2016

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

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Nirmal Bhasu replied | 06/12/2016

The locus of point of intersection of perpendicular tangents to the hyperbola is a circle concentric with hyperbola and it is called as director circle. The equation of director circle of hyperbola x^2/a^2 -y^2/b^2 =1 is x^2+y^2=a^2-b^2.

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

What is the equation of chord joining two points on the hyperbola?

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Sudeesh replied | 26/11/2016

xy1 + yx1 = 2c * c.

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Ankit replied | 09/12/2016

xy1 + yx1 = 2c * c.

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

What are the equation for finding the coordinates of the point of contact?

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Rachna replied | 21/11/2016

To find the coordinates of point of contact you have to solve the equations simultaneously either by elimination method, or substitution or cross amulet up location method

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Ankit replied | 09/12/2016

To find the coordinates of point of contact you have to solve the equations simultaneously either by elimination method, or substitution or cross amulet up location method.

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

What is the difference between the diameter and conjugate diameter?

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Nirmal replied | 03/12/2016

Hello Sangeetha,
Two diameters are conjugate if each bisects the chords parallel to the other diameter. If you consider the Hyperbola and Parabola, things get a little complicated. It is much simpler in Circles and Ellipses. Consider reading this link if you want to know more.

http:/...  more»
Hello Sangeetha,
Two diameters are conjugate if each bisects the chords parallel to the other diameter. If you consider the Hyperbola and Parabola, things get a little complicated. It is much simpler in Circles and Ellipses. Consider reading this link if you want to know more.

http://www.grad.hr/geomteh3d/skripta/konj_promjeri_eng.html

Regards

Nirmal «less

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Rahul replied | 05/12/2016

Hello Sangeetha,
If we talk about ellipse, any chord that passes through the center of an ellipse is call its diameter. It follows that the family of parallel chords define two diameters: one in the direction to which they are all parallel and the other the locus of their midpoints. Such two diameters are called conjugate.

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

Prove that the midpoints of chords of the hyperbola (square of x)/(square of a)–(square of y)/(square of b) = 1 parallel to the diameter y = mx lie on the diameter (square of a)my = (square of b) x?

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Ankit replied | 09/12/2016

Answer to this question cant be texted. Have a live session with me.

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A

Aravind replied | 12/12/2016

Let the cord parallel to y=mx be
y=mx+c..............(1)
Then the points of intersection with the hyperbola are given by:-

x^2/a^2 - (mx+c)^2/b^2 = 1
or (1/a^2-m^2/b^2)x^2-2mxc/b^2-c^2/b^2-1=0 .....(2)

Let (x1,y1) and (x2,y2) be the end points of the cord.
Then x1 and x2 both satisfy Eq.(2)

So x1+x2 = [2mc/b^2]/(1/a^2-m^2/b^2)
...  more»
Let the cord parallel to y=mx be
y=mx+c..............(1)
Then the points of intersection with the hyperbola are given by:-

x^2/a^2 - (mx+c)^2/b^2 = 1
or (1/a^2-m^2/b^2)x^2-2mxc/b^2-c^2/b^2-1=0 .....(2)

Let (x1,y1) and (x2,y2) be the end points of the cord.
Then x1 and x2 both satisfy Eq.(2)

So x1+x2 = [2mc/b^2]/(1/a^2-m^2/b^2)
= 2mc/(b^2/a^2-m^2)...............(3)

Let (h,k) be the midpoint of the cord. Then
h=(x1+x2)/2 = mc/(b^2/a^2-m^2)
and k=(y1+y2)/2.

Now both (x1,y1) and (x2,y2) satisfy Eq(1) so that
k=mh+c. Substituting the value of c from Eq(3)
k=mh+(b^2/a^2-m^2)h/m = b^2/(a^2m)
Or a^2 mk = b^2h
Therefore the locus of the midpoint (h,k) of the cord
is a^2 my = b^2x. «less

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

Prove that the angle subtended by any chord of a rectangular hyperbola at the centre is the supplement of the angle between the tangents at the end of the chord?

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Ankit replied | 09/12/2016

Solve with the help of parametric equations of hyperbola.

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Mohit replied | 14/12/2016

Solve with the help of parametric equations of hyperbola.

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

On a level plain the crack of the rifle and the thud of the ball striking the target are heard at the same instant, prove that the locus of the hearer is a hyperbola?

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Jaya Laxmi Kl replied | 24/11/2016

Please find the solution screenshot.

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

Find the locus of intersection of tangent to a hyperbola, which meet at a constant angle x?

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Rita replied | 22/11/2016

Equation of hyperbola is x2/a2-y2/b2 = 1

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

Find the equation to the hyperbola whose asymptotes are the straight lines x + 3y – 1= 0 and 2x – y + 7 = 0, and which passes through the point (1, 2)?

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Chirag replied | 23/11/2016

Asymptotes are nothing but tangents at infinity take equation of tangents and solve it.

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Chirag replied | 23/11/2016

Let equation of the hyperbola is (x-h)^2/a^2+(y-b)^2/b^2 and its asymptotes are given by:- y=+or-(b/a)(x-h)+k.
You can compare your equations with this and find relevant values of a, b, h, k and substitute in equation of hyperbola.

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