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

The equation of the line which passes through \mathrm{\left(\text { a } \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

d

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

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

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

\mathrm{\therefore } Equation of required line is 

         \mathrm{y-a \sin ^3 \theta=(\cos \theta / \sin \theta)\left(x-a \cos ^3 \theta\right)}

or  \mathrm{x \cos \theta-y \sin \theta=a\left(\cos ^4 \theta-\sin ^4 \theta\right)}

\mathrm{=a\left(\cos ^2 \theta+\sin ^2 \theta\right)\left(\cos ^2 \theta-\sin ^2 \theta\right)}

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

Hence correct answer id (d)

 

Posted by

avinash.dongre

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