Equation of the line passing through the point `(acos^3theta, a sin^3theta)` and perpendicular to the line `xsectheta + y cosec theta =a` is `xcostheta-ysintheta =asin2theta`.

Answer

B

Explanation

We have `y=(-x sectheta)/("cosec"theta)+(a)/("cosec"theta)`
`implies" Slope"=-(sectheta)/("cosec "theta)`
`therefore` Required equation of line is
`y-a sin^(3)theta=("cosec "theta)/(sec theta)(x- a cos^(3)theta)`
`impliesy-a sin^(3)theta=(costheta)/(sectheta)(x-acos^(3)theta)`
`impliesysintheta-asin^(4)theta`
`=xcostheta-a cos^(4)theta`
`impliesxcostheta-ysintheta+asin^(4)theta-acos^(4)theta=0`
`impliesx costheta-y sintheta-a cos 2 theta=0`