Q. If $( - 3,\ 2)$ lies on the circle $x^{2} + y^{2} + 2gx + 2fy + c = 0$ which is concentric with the circle $x^{2} + y^{2} + 6x + 8y - 5 = 0$, then $c$ is equal to
A) 11
B) $- 11$
C) 24
D) 100
Explanation
(b)
Equation of family of concentric circles to the circle $x^{2} + y^{2} + 6x + 8y - 5 = 0$ is
$x^{2} + y^{2} + 6x + 8y + \lambda = 0$
Which is similar to $x^{2} + y^{2} + 2gx + 2fy + c = 0$
Thus, the point $( - 3,\ 2)$ lies on the circle
$x^{2} + y^{2} + 6x + 8y + c = 0$
$\therefore\ \ ( - 3)^{2} + (2)^{2} + 6( - 3) + 8(2) + c = 0\ \Rightarrow c = - 11$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.