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 $(-1,0)$
$\therefore 1+4-\lambda =0\Rightarrow \lambda =5$
$\therefore x^2+y^2+5x-4y+4=0$
Put $y=0\Rightarrow x=-1,-4$
$\therefore$ Circle passes through $(-4,0)$