Question

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

• A. $x+y+a=0$
• B. $x=0$
• C. $x=a$
• D. $x-y+a=0$

Answer 1

The correct option is B $x=0$

Let the equation of tangent to the parabola be $y=mx+\frac{a}{m}$

Since, it is also a tangent to $x^2+y^2=4ax$

Therefore, radius = perpendicular distance

$2a=\frac{2ma+\frac{a}{m}}{\sqrt{1+m^2}}$

Solving for m we get equation of tangent $x=0$