Question

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

• 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

$(\frac{1}{2},-\sqrt{2})$

Let the centre of the circle be (x, y)

$x=\frac{0+1}{2}$

$=\frac{1}{2}$

$r=\frac{3}{2}$

$\sqrt{x^2+y^2}=\frac{3}{2}$

$y=\pm \sqrt{2}$

So there are two circles possible.