Q. If $g^{2} + f^{2} = c$, then the equation $x^{2} + y^{2} + 2gx + 2fy + c = 0$ will represent
A) A circle of radius $g$
B) A circle of radius $f$
C) A circle of diameter $\sqrt{c}$
D) A circle of radius zero
Explanation
(d)
Given, $x^{2} + y^{2} + 2gx + 2fy + c = 0$
$\therefore$ Radius of circle $= \sqrt{g^{2} + f^{2} - c}$
$= \sqrt{c - c} = 0\ \ \ \ \ \ \lbrack giveng^{2} + f^{2} = c\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.