Ordinary and radial plots of ellipses.

1. Ordinary and Radial plots of an ellipse.
Sharon Liu.
2023/08/10.
This is helpful, for plotting the rotated sphere.
x^2/a^2 + y^2/b^2 = 1.
a = 2.
b = 1.
y = plusminus sqrt((4-x^2)/4).

2. cos(theta) = d_x/h.
sin(theta) = d_y/h.
We don’t know h (yet).
h = sqrt(d_x^2 + d_y^2).
We could do a simultaneous equation.
y = mx.
h = 1.
m = y/x.
cos(theta) = d_x.
sin(theta) = d_y.
m = d_y/d_x.
We now know m. Put this, into an ellipse equation.
y^2 = (4-x^2)/4.
m^2 – x^2 = (4-x^2)/4.
x^2 = 4/(4m^2 + 1).
x = plusminus sqrt(4/(4m^2 + 1)).
y = plusminus sqrt((4-x^2)/4).