Question

The equation of the circle having $(6,7)$ and $(4,3)$ as the endpoints of its diameter is

• A. $(x^2-y^2-2xy+45=0$
• B. $10(x+y)-2xy+45=0$
• C. $(x+y)\left[\right(x+y)-10]-2xy+45=0$
• D. $(x+y{)}^2-2xy+45=0$

Answer 1

The correct option is C

$(x+y)\left[\right(x+y)-10]-2xy+45=0$

Equation of a circle when the end points $(x_1,y_1)$ and $(x_2,y_2)$ of its diameter are given, is given by,

$(x-x_1)(x-x_2)+(y-y_1)(y-y_2)=0$

So, when $(6,7)$ and $(4,3)$ are the end points of the diameter, equation of the circle would become:

$(x-6)(x-4)+(y-7)(y-3)=0$

$x^2-10x+24+y^2-10y+21=0$

$x^2+y^2-10(x+y)+45=0$

$(x+y{)}^2-2xy-10(x+y)+45=0$

$(x+y)\left[\right(x+y)-10]-2xy+45=0$