The equation of a straight line which passes through the point $\left( {a\;{\rm{co}}{{\rm{s}}^3}{\rm{\theta }},{\rm{\;}}a\;{\rm{si}}{{\rm{n}}^3}{\rm{\theta }}} \right)$ and perpendicular to $x\sec {\rm{\theta }} + y\;{\rm{cosec\;\theta }} = a$ is

$x\cos {\rm{\theta }} - \;y\sin {\rm{\theta }} = - a\cos 2{\rm{\theta }}$

$\frac{x}{a} + \frac{y}{a} = a\cos {\rm{\theta }}$

$x\cos {\rm{\theta }} + y\sin {\rm{\theta }} = a\cos 2{\rm{\theta }}$

$x\cos {\rm{\theta }} + y\sin {\rm{\theta }} - a\cos 2{\rm{\theta }}$

JEE MATHEMATICS MCQ: STRAIGHT LINES

1 Easy

1 of 1

Application +4 | -1

The equation of a straight line which passes through the point

\left( {a\;\mathrm{co}{\mathrm{s}^3}\mathrm{\theta },\mathrm{\;}a\;\mathrm{si}{\mathrm{n}^3}\mathrm{\theta }} \right)

and perpendicular to

x\sec \mathrm{\theta } + y\;\mathrm{cosec\;\theta } = a

View answer and explanation

Correct option: B

x\cos \mathrm{\theta } - \;y\sin \mathrm{\theta } = - a\cos 2\mathrm{\theta }

Option B (

x\cos \mathrm{\theta } - \;y\sin \mathrm{\theta } = - a\cos 2\mathrm{\theta }

) is correct because it represents the equation of a line passing through the given point and perpendicular to the given line.