Question

I hv a prblm in a maths frm tangnt n normal- find the equation of the common tangents to the circle x^2+y^2=8 and the parabola y^2=16x (application of differentiation)

Answer 1

differentiate both curves , then make them equal :P

Answer 2

Common tangents will touch both the circle and the parabola, and the tangent lines will have the same slope.

For the circle, the slope of any tangent line is
\[x^2+y^2=8~~\Rightarrow~~2x+2y\frac{dy}{dx}=0~~\iff~~\frac{dy}{dx}=-\frac{x}{y}\]
For the parabola,
\[y^2=16x~~\Rightarrow~~2y\frac{dy}{dx}=16~~\iff~~\frac{dy}{dx}=\frac{8}{y}\]

Answer 3

Like @BSwan said, set the derivatives equal, you'll have that the slopes of the tangent lines are the same for \(x=-8\).