Question

Assertion(A): The points $(-6,2),(-3,1)$ are a pair of inverse points $w$. r.t. the circle $x^2+y^2=20$
Reason (R): The polar of $(-6,2)$ w.r.t. $x^2+y^2=20$ passes through $(-3,1)$
The correct answer is

• A. Both A and R are true and R is the correct explanation of A
• B. Both A and R are true and R is not the correct explanation of A
• C. A is true but R is false
• D. A is false but R is true

Answer 1

The correct option is B Both A and R are true and R is not the correct explanation of A

Assertion: If $P(-6,2)$ , $Q(-3,1)$ are pair of inverse point w.rt. $x^2+y^2=20$
then $O(0,0)$ , $P$ and $Q$ are collinear points with
$OP,OQ=r^2=20$
$OP=\sqrt{40}$ and $OQ\sqrt{10}$
$\therefore OP\cdot OQ=\sqrt{400}=20$.
Reason: polar of (-6,2) w.rt. $x^2+y^2=20$ is
$x(-6)+y\left(2\right)=20$
$2y-6x=20$
$y-3x=10$
$(-3,1)$ lie on $y+3x+1$ is True but it is not a correct explanation for Assertion.
Hence correct answer is B.