Q. The equation of the chord of the circle, $x^{2} + y^{2} = a^{2}$ having $(x_{1},\ y_{1})$ as its mid point, is
A) $xy_{1} + yx_{1} = a^{2}$
B) $x_{1} + y_{1} = a$
C) $xx_{1} + yy_{1} = x_{1}^{2} + y_{1}^{2}$
D) $xx_{1} + yy_{1} = a^{2}$
Explanation
(c)
If mid point is given, then equation of chord is $T = S_{1}$
$\therefore\ \ xx_{1} + yy_{1} - a^{2} = x_{1}^{2} + y_{1}^{2} - a^{2}$
$\Rightarrow \ \ xx_{1} + yy_{1} = x_{1}^{2} + y_{1}^{2}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.