Q. The line $ax + by + c = 0$ is normal to the circle $x^{2} + y^{2} + 2gx + 2fy + d = 0$, if
A) $ag + bf + c = 0$
B) $ag + bf - c = 0$
C) $ag - bf + c = 0$
D) $ag - bf - c = 0$
Explanation
(b)
The centre of given circle is $( - g,\ - f)$
If the given line $ax + by + c = 0$ is normal to the circle, then it passes through the centre of circle.
$\therefore a\ ( - g) + b( - f) + c = 0\ \Rightarrow ag + bf - c = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.