Home
Class 12
MATHS
A hyperbola having the transverse axis o...

A hyperbola having the transverse axis of length 2 sin `theta` is confocal with the ellipse `3x^(2)+4y^(2)=12.` Then its equation is

A

`x^(2)cosec^(2)theta-y^(2)sec^(2)theta=1`

B

`x^(2)sec^(2)theta-y^(2)cosec^(2)theta=1`

C

`x^(2)sin^(2)theta-y^(2)cos^(2)theta=1`

D

`x^(2)sin^(2)theta-y^(2)cos^(2)theta=1`

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    ARIHANT MATHS|Exercise Hyperbola Exercise 11 : Questions Asked in Previous 13 Years Exams|3 Videos

  • HYPERBOLA

    ARIHANT MATHS|Exercise Hyperbola Exercise 10 : Subjective Type Questions|4 Videos

  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos

  • INDEFINITE INTEGRAL

    ARIHANT MATHS|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 Videos

Similar Questions

Explore conceptually related problems

A series of hyperbola are drawn having a common transverse axis of length 2a. Prove that the locus of point P on each hyperbola, such that its distance from the transverse axis is equal to its distance from an asymptote, is the curve (x^2-y^2)^2 =lambda x^2 (x^2-a^2), then lambda equals

Find the lengths of major and minor axes,the coordinate of foci, vertices and the eccentricity of the ellipse 3x^(2)+2y^(2)=6 . Also the equation of the directries.

If the line 3 x +4y =sqrt7 touches the ellipse 3x^2 +4y^2 = 1, then the point of contact is

Find the equations of the tangents to the ellipse 3x^(2)+4y^(2)=12 which are perpendicular to the line y+2x=4 .

Let a hyperbola passes through the focus of the ellipse (x^(2))/(25)+(y^(2))/(16)=1 . The transverse and conjugate axes of this hyperbola coincide with the major and minor axis of the given ellipse. Also, the product of the eccentricities of the given ellipse and hyperbola is 1. Then,

If the tangent to the ellipse x^2 +4y^2=16 at the point theta normal to the circle x^2 +y^2-8x-4y=0 then theta is equal to

Find the centre, length of the axes, eccentricity and foci of the ellipse : 12x^2+4y^2+ 24x -16y+25=0 .

An ellipse intersects the hyperbola 2x^2-2y =1 orthogonally. The eccentricity of the ellipse is reciprocal to that of the hyperbola. If the axes of the ellipse are along the coordinate axes, then (a) the foci of ellipse are (+-1, 0) (b) equation of ellipse is x^2+ 2y^2 =2 (c) the foci of ellipse are (t 2, 0) (d) equation of ellipse is (x^2 2y)

The foci of a hyperbola coincide with the foci of the ellipse (x^(2))/(25)+(y^(2))/(9)=1 , find the equation of hyperbola if ecentricity is 2.

If, in a hyperbola, the distance between the foci is 10 and the transverse axis has length 8, then the length of its latus-rectum is: