Definition of a circle

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Question

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

Moderate

Solution

Let he equation of the circle be
$(x - k)^{2} + (y - 2)^{2} = k^{2}$
which passes through the point $(- 1, 0)$
if $(- 1 - k)^{2} + 4 = k^{2} \Rightarrow k = - 5 / 2$
and the equation of the circle is
$x^{2} + y^{2} + 5 x - 4 y + 4 = 0$
which passes through $(- 4, 0)$

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