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. $(-2,5)$

Answer 1

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

Let the centre is $(3,k)$ and radius is $k$


The equation of circle is
$(x-3{)}^2+(y-k{)}^2=k^2$
The circle passes through $(1,-2)$
$\Rightarrow (1-3{)}^2+(-2-k{)}^2=k^2$
$\Rightarrow k=-2$
Therefore, equation of circle is
$(x-3{)}^2+(y+2{)}^2=4$
Cleary, $(5,-2)$ is satisfyng the equation of circle.