Equation of the common tangent touching the circle
$(x-3)^2+y^2=9$
and the parabola
$y^2=4x$
above the $x$-axis is
🎥 Video solution / Text Solution of this question is given below:
Let tangent be $y=mx+c$, $m>0$.
Tangency with $y^2=4x$ gives $c=\dfrac1m$.
Tangency with the circle gives $|3m-c|=3\sqrt{m^2+1}$.
Solving gives $m=\dfrac1{\sqrt3},\ c=\sqrt3$.
Equation:
$\sqrt3y=x+3$
Answer: $\boxed{\sqrt3y=x+3}$