Question

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

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

Answer 1

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


As the circle is touching the $x-$axis at $(3,0),$
let the centre of the circle be $C(3,k)$
Radius, $r=|k|$
Equation of the circle is $(x-3{)}^2+(y-k{)}^2=k^2$
Above circle passes through $(1,-2).$
Then, $(1-3{)}^2+(-2-k{)}^2=k^2$
$\Rightarrow k=-2$
Hence, equation of the circle is $(x-3{)}^2+(y+2{)}^2=4$
Clearly, $(5,-2)$ satisfies it.