`The -equation (x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0` Represents a circle whose centre is

Options

A. `((x_1+x_2)/(3),(y_1+y_2)/(3))`
B. `((y_1+x_2)/(2),(x_1+y_2)/(2))`
C. `((x_1+x_2)/(2),(y_1+y_2)/(2))`
D. `((y_1+x_2)/(4),(x_1+y_2)/(4))`

Answer

C

Explanation

Given, `(x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0`,whose extremities of diameter are `(x_1,y_1)` and `(x_2,y_2)`. Hence, coordinates of centre of cricle is `((x_1+x_2)/(2),(y_1+y_2)/(2)).`