The equation to the straight line passing through the point \[(a{{\cos }^{3}}\theta ,\ a{{\sin }^{3}}\theta )\] and perpendicular to the line \[x\sec \theta +y\,\text{cosec}\,\theta =a,\] is [AMU 1975]

\[x\cos \theta +y\sin \theta =a\cos \ 2\theta \]

\[x\cos \theta -y\sin \theta =a\cos \ 2\theta \]

\[x\sin \theta +y\cos \theta =a\cos \ 2\theta \]

The equation to the straight line passing through the point \[(a{{\cos

1.	The equation to the straight line passing through the point \[(a{{\cos }^{3}}\theta ,\ a{{\sin }^{3}}\theta )\] and perpendicular to the line \[x\sec \theta +y\,\text{cosec}\,\theta =a,\] is [AMU 1975]
A.	\[x\cos \theta -y\sin \theta =a\cos \ 2\theta \]
B.	\[x\cos \theta +y\sin \theta =a\cos \ 2\theta \]
C.	\[x\sin \theta +y\cos \theta =a\cos \ 2\theta \]
D.	None of these
Answer» B. \[x\cos \theta +y\sin \theta =a\cos \ 2\theta \]

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The equation to the straight line passing through the point \[(a{{\cos }^{3}}\theta ,\ a{{\sin }^{3}}\theta )\] and perpendicular to the line \[x\sec \theta +y\,\text{cosec}\,\theta =a,\] is [AMU 1975]

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