Home
Class 12
MATHS
The foci of an ellipse are (-2,4) and (2...

The foci of an ellipse are `(-2,4)` and (2,1). The point `(1,(23)/(6))` is an extremity of the minor axis. What is the value of the eccentricity?

A

`(9)/(13)`

B

`(3)/(sqrt(13))`

C

`(2)/(sqrt(13))`

D

`(4)/(13)`

Text Solution

Verified by Experts

The correct Answer is:
B
Foci are `A(-2,4)` and `B(2,1)`
`:. AB = 2ae = 5`
Center is midpoint of AB which is `C(0,5//2)` Distance of center from extremity of minor axis which is `D(1,23//6)` is 'b'
`:. b = (5)/(3)`
Now, `b^(2) = a^(2) - a^(2)e^(2)`
`rArr a^(2) = b^(2) + a^(2)e^(2) = (325)/(36)`
`rArr e^(2) = 1 - (b^(2))/(a^(2)) = (3)/(sqrt(13))`
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

Pa n dQ are the foci of the ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 and B is an end of the minor axis. If P B Q is an equilateral triangle, then the eccentricity of the ellipse is 1/(sqrt(2)) (b) 1/3 (d) 1/2 (d) (sqrt(3))/2

S and T are the foci of an ellipse and B is the end point of the minor axis. If STB is equilateral triangle, the eccentricity of the ellipse is

Find the equation of an ellipse which passes through the point (-2, 2), (3,-1) and the major and minor axes as the axes of co¬ ordinate. Find its eccentricity.

The vertices of an ellipse are (-1,2) and (9,2) . If the eccentricity of the ellipse be (4)/(5) , find its equation .

The eccentricity of an ellipse is (1)/(sqrt(3)) , the coordinates of focus is (-2,1) and the point of intersection of the major axis and the directrix is (-2,3) . Find the coordinates of the centre of the ellipse and also equation of the ellipse .

If the foci of an ellipse are (0,+-1) and the minor axis of unit length, then find the equation of the ellipse. The axes of ellipe are the coordinate axes.

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

Let S and S' be the foci of the ellipse and B be any one of the extremities of its minor axis. If DeltaS'BS=8sq. units, then the length of a latus rectum of the ellipse is

What is the eccentricity of the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 if length of its minor axis is equal to the distance between its foci ?

Find the equation of the ellipse, for which the foci are (0,1) and (0,-1) and length of the minor axis is 1 unit .