Equation of the common tangent to the circle $x^{2} + y^{2} = 4 a x$ and $y^{2} = 4 a x$ is

x + y + a = 0

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x = 0

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x = a

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x - y + a = 0

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Solution

The correct option is B $x = 0$
Let the equation of tangent to the parabola be $y = m x + \frac{a}{m}$
Since, it is also a tangent to $x^{2} + y^{2} = 4 a x$
Therefore, radius = perpendicular distance
$2 a = \frac{2 m a + \frac{a}{m}}{\sqrt{1 + m^{2}}}$
Solving for m we get equation of tangent $x = 0$

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