Question

The centre of the circle passing through (0, 0) and (1, 0) and touching the circle $x^2+y^2=9$ is

• A. $\frac{1}{2},\frac{1}{2}$
• B. $\frac{1}{2},-\sqrt{2}$
• C. $\frac{3}{2},\frac{1}{2}$
• D. $\frac{1}{2},\frac{3}{2}$

Answer 1

The correct option is B $\frac{1}{2},-\sqrt{2}$



From the figure, we get $\sqrt{{\left(\frac{1}{2}\right)}^2+{\lambda }^2}=\frac{3}{2}\Rightarrow \lambda =\pm \sqrt{2}$
Hence, the centres of the circles are
$(\frac{1}{2},\pm \sqrt{2})$