Home
Class 12
MATHS
An ellipse has the points (1, -1) and (2...

An ellipse has the points `(1, -1) and (2,-1)` as its foci and `x + y = 5` as one of its tangent then the value of `a^2+b^2` where `a,b` are the lenghta of semi major and minor axes of ellipse respectively is :

A

`(41)/(2)`

B

10

C

19

D

`(81)/(4)`

Text Solution

Verified by Experts

The correct Answer is:
D
`2ae = SS' =1`
`p_(1)p_(2) = b^(2)`, where `p_(1)` and `p_(2)` are the length of perpendicular from S and S' to the tangent
`(5)/(sqrt(2)). (4)/(sqrt(2)) = b^(2)`
`rArr b^(2) = 10`
`rArr b^(2) = 10 = a^(2) - e^(2)a^(2)`
`rArr a^(2) = (41)/(4)`
Promotional Banner

Topper's Solved these Questions

  • ELLIPSE

    CENGAGE PUBLICATION|Exercise Multiple Correct Answers Type|6 Videos

  • DOT PRODUCT

    CENGAGE PUBLICATION|Exercise DPP 2.1|15 Videos

  • EQAUTION OF STRAIGHT LINE AND ITS APPLICATION

    CENGAGE PUBLICATION|Exercise DPP 3.2|13 Videos

Similar Questions

Explore conceptually related problems

An ellipse has O B as the semi-minor axis, F and F ' as its foci, and /_F B F ' a right angle. Then, find the eccentricity of the ellipse.

An ellipse passes through the point (2,3) and its axes along the coordinate axes, 3x +2y -1 = 0 is a tangent to the ellipse, then the equation of the ellipse is

Taking major and minor axes as x and y -axes respectively, find the equation of the ellipse whose lengths of major and minor axes are 6 and 5 respectively .

Find the equation of the ellipse whose foci are (2, 3) and (-2, 3) and whose length of semi minor axis is sqrt5

An ellipse passing through the origin has its foci (3, 4) and (6, 8). The length of its semi-minor axis is bdot Then the value of b/(sqrt(2)) is____

An ellipse has OB as a semi-minor axis, F and F' are its two foci and the angle FBF' is a right angle. Find the eccentricity of the ellipse.

Find the coordinates of the foci, the vertices, the lengths of major and minor axes and the eccentricity of the ellipse 9x^(2)+4y^(2)=36

Equations of the tangent and the normal drawn at the point (6, 0) on the ellipse (x^(2))/(36) + (y^(2))/(9 )= 1 respectively are-

(5,-4) and (-3, 2) are two foci of an ellipse whose eccentricity is 2/3. Then the length of the minor axis of the ellipse is-

The straight line x + y = a will be a tangent to the ellipse (x^(2))/(9) + (y^(2))/(16) = 1 if the value of a is -