<s>[INST] equation of common tangent touching circle and the parabola I am trying to find the 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 :
Equation of tangent on parabola: $y=mx+a/m$ here a = 1;
so $y = mx + 1/m$
centre of the circle (3,0) and r = 3. Now
distance of point from line is,  $3 = |3m+1/m|/(1+m^2)^(1/2)$
I am having difficulty in finding the value of m. Please help me!!!
 [/INST] \begin{align}
\frac{\displaystyle \left|3m+\frac{1}{m}\right|}{\sqrt{m^2+1}}&=3\\
\left(3m+\frac{1}{m}\right)^2&=9(m^2+1)\\
9m^2+6+\frac{1}{m^2}&=9m^2+9\\
\frac{1}{m^2}&=3\\
m&=\frac{\pm1}{\sqrt{3}}
\end{align}
</s>