Question

The circle passing through the point $(-1,0)$ and touching the $y$-axis at $(0,2)$ also passes through the point

• A. $\left(-\frac{3}{2}, 0\right)$
• B. $\left(-\frac{5}{2}, 2\right)$
• C. $\left(-\frac{3}{2}, \frac{5}{2}\right)$
• D. $(-4,0)$

Answer 1

Answer: (D)

Circle touching $y$-axis at $(0,2)$ is $( x -0)^{2}+( y -2)^{2}+\lambda x =0$
passes through $(-1,0)$
$\therefore 1+4-\lambda=0 \Rightarrow \lambda=5$
$\therefore x^{2}+y^{2}+5 x-4 y+4=0$
Put $y =0 \Rightarrow x =-1,-4$
$\therefore $ Circle passes through $(-4,0)$