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.