How to calculate ellipse sector area *from a focus* How do you calculate the area of a sector of an ellipse when the angle of the sector is drawn from one of the focii? In other words, how to find the area swept out by the true anomaly? There are some answers on the internet for when the sector is drawn from the center of the ellipse, but not from the focii.

Ben, here's a better suggestion. You can stretch a circle to make an ellipse and, if you start with a unit circle, area is magnified by the factor of $ab$, where $a$ and $b$ are the semi-axes, as usual. Take a point at $(-R,0)$ inside the unit circle and consider the sector it subtends to $(1,0)$ and $(\cos t, \sin t)$. You can find the area pretty easily: I get $\frac 12(t+R\sin t)$. Now stretch by the fudge factor and figure out how to match up $R$ with your focus and $t$ with your arbitrary point on the ellipse.