Question

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

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

Answer 1

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

$(-2,4)$ and touches the y-axis at $(0,2)$
Radius of circle $=2$ units
From the figure we can see that $(-2,4)$ is the end point of diameter whose other end is $(-2,0).$
So, centre $D$ of this circle is $(-2,2).$
By subsituting the point $(-2,2)$ in the equations given in the options,
we can see that, only $2x-3y+10=0$ passes through $(-2,2).$