The equation (x - x1) (x - x2) + (y - y1 ) ( y - y2) =0 represents a circle whose centre is

Question

The equation (x - x1) (x - x2) + (y - y1 ) ( y - y2) =0 represents a circle whose centre is (A) ((x1-x2/2), (y1-y2/2)) (B) ((x1 + x2/2), (y1 + y2/2)) (C) (x1, y1) (D) (x2, y2)

Tardigrade Admin · Accepted Answer

Given equation of circle is (x-x1)(x -x2)+(y -y1)(y-y2) = 0 Whose extremities of diameter are (x1, y1) and (x2, y2). ∴ Coordinates of centre of circle is ((x1+x2/2), (y1+y2/2)).

Q. The equation $(x - x_{1}) (x - x_{2}) + (y - y_{1}) (y - y_{2}) = 0$ represents a circle whose centre is

$(\frac{x _{1} - x _{2}}{2}, \frac{y _{1} - y _{2}}{2})$

$(\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})$

$(x_{1}, y_{1})$

$(x_{2}, y_{2})$

Given equation of circle is

$(x - x_{1}) (x - x_{2}) + (y - y_{1}) (y - y_{2}) = 0$

Whose extremities of diameter are $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ .

$∴$ Coordinates of centre of circle is

$(\frac{x _{1} + x _{2}}{2}, \frac{y _{1} + y _{2}}{2})$ .

Q. The equation (x−x1​)(x−x2​)+(y−y1​)(y−y2​)=0 represents a circle whose centre is

(2x1​−x2​​,2y1​−y2​​)

(2x1​+x2​​,2y1​+y2​​)

(x1​,y1​)

(x2​,y2​)