Question

Assertion :The power of the point $(2,3)$ w. r. to the circle $x^2+y^2+4x+2y-3$ is $24$. Reason: The power of circle is equal to the square of the length of its tangent drawn from a point.

• 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 A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

Let $S=x^2+y^2+4x+2y-3$
$\therefore S_1=$ length of tangent from (2, 3) to
the circle S.$=\sqrt{2^2+3^2+4\left(2\right)+2\left(3\right)-3}$
$=\sqrt{4+9+8+6-3}=\sqrt{24}$
$\therefore$ Power of given point w.r.t the circles is $=(\sqrt{24}{)}^2$
Clearly Assertion is followed by Reason.