Question

Assertion :The locus of the point of intersection of the tangents to the circle $x=a\cos \theta ,y=a\sin \theta$ at points whose parametric angles differ by $\pi /2$ is $x^2+y^2=2a^2$ Reason: Tangents at the extremities of a diameter
of a circle are parallel

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Both Assertion and Reason are incorrect

Answer 1

The correct option is B Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion

$x\cos \theta +y\sin \theta =a$,
$x\cos (\frac{\pi }{2}+\theta )+y\sin (\frac{\pi }{2}+\theta )=a\Rightarrow {(x\cos \theta +y\sin \theta )}^2+{(-x\sin \theta +y\cos \theta )}^2={2a}^2\Rightarrow x^2+y^2={2a}^2$
$\Rightarrow$ assertion is true,
Reason is also true but does not lead to assertion