What are the equations for finding common tangents between two curves?

[labinojha]

Homework Statement

Finding the equations of common tangents of $y^{2}$=4ax and $x^{2}$=4by

Homework Equations

Equating both curves' derivatives :
$\frac{2a}{y}$=$\frac{x}{2b}$

The Attempt at a Solution

Calculated both of the curves' derivatives and equated them .
Used the resulting relation in two point form of straight line equation (y-y1)=m(x-x1) .

Got Stuck now! with too many cuberoots .

 

[SammyS]

In your equation: $\displaystyle \frac{2a}{y}=\frac{x}{2b}\,,$ the y is from a point on the first curve, the x from a point on the second curve.

Instead, start by doing the following:

Find the general equation for a line tangent to y²=42x.

The find the general equation for a line tangent to x²=4by.