Question

A circle is drawn touching the $x$-axis. with its centre at the point of reflection of $(m, n)$ on the line $y-x=0$. Then the equation of the circle is

• A. $x^{2}+y^{2}-2 m x-2 n y+ m^{2}=0$
• B. $x^{2}+y^{2}-2 m x+2 n y+ m^{2}=0$
• C. $x^{2}+y^{2}+2 n x-m y-n^{2}=0$
• D. $x^{2}+y^{2}-2 n x-m y +n^{2}=0$

Answer 1

Answer: (D)

The point of reflection of $(m, n)$ on the line
$y-x=0$ is $(n, m)$, so equation of circle having centre $(n, m)$ and let radius $r$ is
$(x-n)^{2}+(y-m)^{2}=r^{2} \ldots . .$ (i)
$\because$ Circle (i) touches the $X$-axis, so $r=m$
So, equation of required circle is
$(x-n)^{2}+(y-m)^{2}=m^{2}$
or $x^{2}+y^{2}-2 n x-2 m y+ n^{2}=0$