Question

A circle passes through $(-2,4)$ and touches the $y-$axis at $(0,2).$ Then which of the following equations can represent a diameter of the circle?

• A. $4x+5y-6=0$
• B. $2x-3y+10=0$
• C. $3x+4y-3=0$
• D. $5x+2y+4=0$

Answer 1

The correct option is B $2x-3y+10=0$


Let centre of the circle be $(h,k)$
As it touches $y-$axis at $(0,2),$ then
$k=2$ and $r=|h|$

Also, $(-2,4)$ lies on the given circle, so distance between the point and centre is equal to radius.
$\Rightarrow \sqrt{(h+2{)}^2+(2-4{)}^2}=r\Rightarrow h^2+4+4h+4=h^2\Rightarrow h=-2$
So, centre is $(-2,2),$ which lies on the line $2x-3y+10=0$
Hence, $2x-3y+10=0$ is one of the diameters of the circle.