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  • The equation of the line which passes through <img alt="\mathrm{\text { (a } \left.\cos ^3 \theta, \text { a } \sin ^3 \theta\right)}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cm

The equation of the line which passes through \mathrm{\text { (a } \left.\cos ^3 \theta, \text { a } \sin ^3 \theta\right)} and

perpendicular to the line  \mathrm{x \sec \theta+y \operatorname{cosec} \theta=a} is 

 

Option: 1

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


Option: 2

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


Option: 3

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


Option: 4

None of these


Answers (1)

best_answer

Slope of line \mathrm{x \sec \theta+y \operatorname{cosec} \theta=a} 

is \mathrm{-\sec \theta / \operatorname{cosec} \theta=-\sin \theta / \cos \theta}

\mathrm{\therefore \text { Slope of line } \perp \text { to this line }=\cos \theta / \sin \theta}

Equation of required line is

\mathrm{\begin{aligned} & y-a \sin ^3 \theta=(\cos \theta / \sin \theta)\left(x-a \cos ^3 \theta\right) \\ & \text { or } x \cos \theta-y \sin \theta=a\left(\cos ^4 \theta-\sin ^4 \theta\right) \\ & =a\left(\cos ^2 \theta+\sin ^2 \theta\right)\left(\cos ^2 \theta-\sin ^2 \theta\right) \\ & \text { or } x \cos \theta-y \sin \theta=a \cos 2 \theta \end{aligned}}

Hence correct answer is (d)

 

 

 

Posted by

Pankaj

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