Question

The circle passing through $(1,-2)$ and touching the axis of $x$ at $(3,0)$ also passes through the point:

• A. $(-5,-2)$
• B. $(2,-5)$
• C. $(5,-2)$
• D. $(-5,2)$

Answer 1

The correct option is C $(5,-2)$

Let the equation of the circle is-

${(x-h)}^2+{(y-k)}^2=r^2⟶\left(i\right)$

when circle touches $x$ axis then $r=k$

substituting $(1,-2)$ in ${eq}^n\left(i\right)$ and $r=k$, we get

$h=3,k=-2\&r=2$

${(x-3)}^2+{(y+2)}^2=4$

Since $(5,-2)$ is the only point which satisfies the equation.

Hence, $(5,-2)$ is the correct answer.