A) a straight line
B) a circle
C) a pair of straight line
D) None of the above
Correct Answer: B
Solution :
We have, the given circle\[x=a\cos \theta ,\,\,y=a\sin \theta \] \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] ... (i) Tangents to the circle (i) at\[\theta \]and\[\left( \theta +\frac{\pi }{2} \right)\]are \[x\cos \theta +y\sin \theta =a\] and \[x\cos \left( \theta +\frac{\pi }{2} \right)+y\sin \left( \theta +\frac{\pi }{2} \right)=a\] or \[x\cos \theta +y\sin \theta =a\] and \[-x\sin \theta +y\cos \theta =a\] Squaring and adding, we get\[{{x}^{2}}+{{y}^{2}}=2{{a}^{2}}\] which is a circle.
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