Q. The equation $\left( x - x_{1} \right)\left( x - x_{2} \right) + \left( y - y_{1} \right)\left( y - y_{2} \right) = 0$ represents a circle whose centre is
A) $\left( \frac{x_{1} - x_{2}}{2},\ \frac{y_{1} - y_{2}}{2} \right)$
B) $\left( \frac{x_{1} + x_{2}}{2},\ \frac{y_{1} + y_{2}}{2} \right)$
C) $(x_{1},\ y_{1})$
D) $(x_{2},\ y_{2})$
Explanation
(b)
Given, $\left( x - x_{1} \right)\left( x - x_{2} \right) + \left( y - y_{1} \right)\left( y - y_{2} \right) = 0$
Whose extremities of diameter are $(x_{1},\ y_{1})$ and $(x_{2},\ y_{2})$
$\therefore$ Coordinates of centre of circle is $\left( \frac{x_{1} + x_{2}}{2},\ \frac{y_{1} + y_{2}}{2} \right)$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.