Question

If a circle passing through the point $(-1,0)$ touches y-axis at $(0,2)$, then the length of the chord of the circle along the x-axis is

• A. $\frac{5}{2}$
• B. $5$
• C. $\frac{3}{2}$
• D. $3$

Answer 1

The correct option is D $3$

Since the required circle touches y-axis at $(0,2)$ and let $r$ be the radius of the circle.
So, the center will be $(-r,2)$.
Equation of circle is
$(x+r{)}^2+(y-2{)}^2=r^2$

Since, it passes through $(-1,0)$,

$\Rightarrow (r-1{)}^2+4=r^2$

$\Rightarrow r=\frac{5}{2}$

So the center is $(-\frac{5}{2},2)$

Now, the perpendicular from the center of the circle to the chord bisects the chord.

So, $AB=2AM$

Coordinates of $M$ is $(-\frac{5}{2},0)$

So, $AM=\frac{3}{2}$

$\Rightarrow AB=3$