Find the equations of the common tangents to the parabola $y^2=15x$ and the circle $x^2+y^2=16$. The text says:

Find the equations of the common tangents to the parabola $y^2=15x$ and the circle $x^2+y^2=16$.

I tried the approach of the discriminant and also one using the distance from a line but both didn't work for me. A previous exercise asked me to demonstrate that the line $y=mx+\frac{15}{4m}$ is a tangent to the parabola for every value of $m$. A suggestion in the text says I can use this result also to find the common tangent.

HINT:
To tackle the second part together it is better to use symbols throughout.
Circle tangent is 
$$ x x_1 + y y_1 = a^2, slope= \frac {x_1}{y_1} $$
Parabola  is 
$$ y^2 = 4 f x $$ 
Differentiate the above for parabola
$$ y^{\prime}_{par} = 2 f/y_{par} $$
Equating common slopes we get 
$$ x_{par} = 2f,\, y_{par} = 2 \sqrt2\, f $$
Verify the above. Can you now take it further (to find equation to a line passing through above point and given slope) ?
