# Another ellipse question...

• December 19th 2007, 08:29 AM
free_to_fly
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.

The midpoint of the straight line joining $P(a\cos{t},b\sin{t})$ and $A(a,0)$ is
$M\left(\frac{a\cos{t}+a}{2},\frac{b\sin{t}+0}{2}\r ight)$
$x\ =\ \frac{a}{2}\,(\cos{t}+1)$
$y\ =\ \frac{b}{2}\,\sin{t}$