Home
Class 12
MATHS
What is the ratio of the greatest and le...

What is the ratio of the greatest and least focal distances ofa point on the ellipse `4x^(2)+9y^(2)=36?`

Text Solution

Verified by Experts

The correct Answer is:
`(7+3sqrt(5))/(2)`
Given ellipse is `(x^(2))/(9)+(y^(2))/(4)=1(agtb)`.
`a^(2)=9,b^(2)=4,e=sqrt((a^(2)-b^(2))/(a^(2)))=sqrt((9-4)/(9))=sqrt(5)/(4)`
Greatest focal distane a=+ae
Least focal distance =a-ae
`:.` Required ratio `(a+ae)/(a-ae)+(1+e)/(a-e)`
`=(1+(sqrt(5))/(3))/(1-(sqrt(5))/(3))=(3+sqrt(5))/(3+sqrt(5))`
`=((3+sqrt(5))^(2))/(4)=(7+3sqrt(5))/(2)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the sum of the focal distance of any point on the ellipse 9x^(2) +25y^(2) = 225 .

The sum of the focal distances of any point on the ellipse 4x^(2) + 25y = 100 is_

Find the sum of the focal distances of any point on the ellipse 9x^2+16 y^2=144.

The sum of the focal distances of any point on the conic 16x^(2) + 25 y ^(2)=400 is-

The length of major axis of the ellipse 4x^(2) + 9y^(2) = 36 is _

Find the area of the greatest rectangle that can be inscribed in an ellipse (x^2)/(a^2)+(y^2)/(b^2)=1 .

Find the number of rational points on the ellipse (x^2)/9+(y^2)/4=1.

Show that the difference of the focal distances of any point on the hyperbola 9x^(2) - 16y^(2) = 144 is equal to its transverse axis.

Find the equations of the tangents drawn from the point (2, 3) to the ellipse 9x^2+16 y^2=144.

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-