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if the line x- 2y = 12 is tangent ...

if the line x- 2y = 12 is tangent to the ellipse `(x^(2))/(b^(2))+(y^(2))/(b^(2))=1` at the point `(3,(-9)/(2))` then the length of the latusrectum of the ellipse is

A

9

B

`8sqrt(3)`

C

5

D

`12sqrt(2)`

Text Solution

Verified by Experts

The correct Answer is:
A
Given equation of ellipse is `x^(2)/a^(2) + y^(2)/b^(2)=1`…………(i)
Equation of tangent at `(3,-9/2)`
`(3x)/a^(2) +(-9/2)/b^(2)=1`
But the tangent is given by
x-2y=12………(ii)
So (i) and (ii) must be identical
`a^(2)/3 =12` and `-2/9b^(2) =(2 xx 27)/6 =9`
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