Question

Assertion :The chords of contact of the pair of tangents drawn from each point on the line $2x+y=4$ to the circle $x^2+y^2=1$ pass through the point $(1/2,1/4)$. Reason: The locus of the point of intersection of the tangents at the extremities of any chord of a circle $C$, passing through a point P is the polar of $P$ with respect to the circle $C$ and $P$ is the pole of its polar.

• 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

The point $(\frac{1}{2},\frac{1}{4})$ is the pole of line $2x+y=4$ wrt the circle. Hence, all chords of contact pass through this point. Hence, assertion and reason are both true. But, the reason given is opposite in meaning to what is required to explain the assertion and hence, is not the correct explanation.