Question

If $N$ is the normal to the circle $x^2+y^2+4x+6y-39=0$ at the point $(2,3)$, then it meets the circle again at

• A. $(2,9)$
• B. $(-6,3)$
• C. $(2,-9)$
• D. $(-6,-9)$

Answer 1

The correct option is D $(-6,-9)$

Let the other point be $P(h,k)$
Given point is $(2,3)$ and the centre of the circle is $(-2,-3)$
Now, we know that centre is midpoint, so
$(-2,-3)=(\frac{h+2}{2},\frac{k+3}{2})\Rightarrow h=-6,k=-9$