JEE Advanced 2011 Paper 2Question 1
The circle passing through the point $(-1,0)$ and touching the $y$-axis at $(0,2)$ also passes through the point
Circle
Solution
Touching the $y$-axis at $(0,2)$ gives centre $(h,2)$, radius $|h|$. Through $(-1,0)$: $(1+h)^2+4=h^2$, so $h=-\frac52$, radius $\frac52$. Check $(-4,0)$: $\left(-\frac32\right)^2+4=\frac{25}{4}$. Yes.