The centre of the circle passing through (0,0) and (1,0) and touching the circle

Question -

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

Options:

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: Option B
:
B
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.

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