Question

the value of `lambda` for which the line `2x-8/3lambday=-3` is a normal to the conic `x^2+y^2/4=1` is:
A. `(3)/(8)`
B. `(1)/(2)`
C. `-(sqrt(3))/(2)`
D. `(sqrt(3))/(2)`

Answer 1

Correct Answer - 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)`