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Find the values of lambda for which the ...

Find the values of `lambda` for which the line `2x-(8)/(3)lamda y=-3` is a normal to the ellipe `x^(2)+(y^(2))/(4)=1`

A

`(3)/(8)`

B

`(1)/(2)`

C

`-(sqrt(3))/(2)`

D

`(sqrt(3))/(2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Equation of normal to ellipse `x^(2) + (y^(2))/(4) =1` is
`(x)/(cos theta) -(2y)/(sin theta) =1 -4` (i)
Comparing with `2x -(8)/(3) lambda y =- 3`
`cos theta =(1)/(2), lambda = (3)/(4 sin theta) = (sqrt(3))/(2)`
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