Question

The equation of the circumcircle of the square formed by the lines $x^{2}-8x+12=0$ and $y^{2}-14y+45=0$ is

• A. $x^{2}+y^{2}-4x-7y+57=0$
• B. $x^{2}+y^{2}-8x-14y+57=0$
• C. $x^{2}+y^{2}-8x-\left|14 y + 5\right|=0$
• D. $2x^{2}+y^{2}-8x-14y+57=0$

Answer 1

Answer: (B)

The given equation of lines are $\left(x - 2\right)\left(x - 6\right)=0,\left(y - 5\right)\left(y - 9\right)=0$
i.e. $x=2,x=6,y=5,y=9$

Circle with segment joining $\left(2,5\right)$ and $\left(6,9\right)$ as the diameter is $\left(x - 2\right)\left(x - 6\right)+\left(y - 5\right)\left(y - 9\right)=0$