# Common tangents equations

1. Aug 6, 2011

### labinojha

1. The problem statement, all variables and given/known data

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

2. Relevant equations

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

3. 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 .

2. Aug 6, 2011

### SammyS

Staff Emeritus
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.

Last edited: Aug 6, 2011