Iso-Optic Curve of the Ellipse
This Demonstration shows an ellipse (red), and two other curves (blue), from which the ellipse subtends the angles (further from the ellipse) and (closer to the ellipse).
Given an ellipse with semi-major and semi-minor axes and , we look for viewpoints from which the ellipse subtends the angle . We start from the point on the ellipse; this will be one of the tangent points. Next we calculate the two possible viewpoints , ; from one of them the ellipse subtends the angle , from the other one the ellipse subtends the angle . As the parameter goes from 0 to we get the set of viewpoints for those two angles, which form the two iso-optic curves of the ellipse.
You can set the ellipse parameters and to between 1 and 10, and between 5° and 90°. The first snapshot shows the iso‐optic curve in general. From the second snapshot you can see that if is small, the curve looks like a circle. In the third snapshot, , so the curve is a circle.