Home
Class 12
MATHS
Find the eccentricity of an ellipse bewe...

Find the eccentricity of an ellipse beween whose foci is 10 and that between focus and corresponding directirx is 15

Text Solution

Verified by Experts

The correct Answer is:
`(1)/(2)`

W have 2ae =10 or ae=5
and `(a)/(e)-ae=15`
`rArr(5)/(e^(2))-5=15`
`rArr(5)/(e^(2))=20`
`:. e=(1)/(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the equation of the ellipse whose one of the foci is (2,0) and the corresponding directrix is x = 8 and eccentricity is (1)/(2) .

Find the equation of the ellipse whose focus is S(+-1, -1), the corresponding directrix is x -y+3=0, and eccentricity is 1/2. Also find its center, the second focus, the equation of the second directrix, and the length of latus rectum.

Prove that in an ellipse, the perpendicular from a focus upon any tangent and the line joining the centre of the ellipse to the point of contact meet on the corresponding directrix.

Prove that in an ellipse, the perpendicular from a focus upon any tangent and the line joining the centre of the ellipse to the point of contact meet on the corresponding directrix.

On the x-y plane, the eccentricity of an ellipse is fixed (in size and position) by 1) both foci 2) both directrices 3)one focus and the corresponding directrix 4)the length of major axis.

Find the equation of the ellipse whose eccentricity is 1/2 , one of the foci is (2, 3) and a directrix is x = 7. Also find the length of the major and minor axes of the ellipse.

find the eccentricity of the ellipse with foci on x-axis if its latus be equal to one half f of its major axis.

Find the equation of an ellipse whose axes are the x-and y-axis and whose one focus is at (4,0) and eccentricity is 4/5.

Find the equation of the hyperbola in each of the cases given below : (i) foci ( -+2,0) eccentricity = 3/2 (ii) Centre ( 2, 1) one of the foci (8,1) and corresponding directrix x = 4. (iii) Passing through ( 5,-2) and length of the transverse axis along x axis and of length 8 units.