Question

The line passing through `(-1,pi/2)` and perpendicular to `sqrt3 sin(theta) + 2 cos (theta) = 4/r` is
A. `2 = sqrt(3)r cos theta - 2r sin theta`
B. `5 =- 2sqrt(3)r sin theta +4r cos theta`
C. `2 = sqrt(3)r cos theta +2r cos theta`
D. `5 = 2 sqrt(3)r sin theta +4r cos theta`

Answer 1

Correct Answer - A
Perpendicular to `sqrt(3) sin theta +2 cos theta = (4)/(r)` is
`sqrt(3) sin ((pi)/(2) +theta) +2 cos ((pi)/(2)+theta) = (k)/(r )`
It is passing through `(-1,pi//2)`
`:. sqrt(3) sin pi +2 cos pi =(k)/(-1) rArr k = 2`
`:. sqrt(3) cos theta - 2 sin theta = (2)/(r) rArr 2 = sqrt(3)r cos theta - 2r sin theta = 2`.