Question

The equation $(x - x_1) (x - x_2) + (y - y_1 ) ( y - y_2) =0$ 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. $(x_2, y_2)$

Answer 1

Answer: (B)

Given equation of circle is

$\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 $\left(x_{1}, y_{1}\right)$ and $\left(x_{2}, y_{2}\right)$.


$\therefore $ Coordinates of centre of circle is

$\left(\frac{x_{1}+x_{2}}{2}, \frac{y_{1}+y_{2}}{2}\right)$.