# Math Help - Another ellipse question...

1. ## Another ellipse question...

I'm stuck on yet another problem...

The point P(acost, bsint) on the ellipse with the equation:
x^2/(a^2)+y^2/(b^2)=1
is joined to the point A (a.0) and M is the mid-point of AP. As t varies, find a cartesian equation of the locus of M.

2. The midpoint of the straight line joining $P(a\cos{t},b\sin{t})$ and $A(a,0)$ is

$M\left(\frac{a\cos{t}+a}{2},\frac{b\sin{t}+0}{2}\r ight)$

So, for the locus of M, we have

$x\ =\ \frac{a}{2}\,(\cos{t}+1)$

$y\ =\ \frac{b}{2}\,\sin{t}$

Eliminate t and you have the Cartesian equation for the locus of M.