I have an ellipse with focal points at $(-2,0)$ and $(2,0)$ and one of the tops is at $(0,4)$. I need to determine an equation of ellipse in form like $ax^2 + by^2 - c = 0$ based on this information. I can't figure out how to do that. Could I have some advise on the problem? Thanks.
Found the solution thanks to @Tavish which is:
$4x^2 + 5y^2 - 80 = 0$
What you describe is a standard ellipse. The foci are located at $(\pm ae,0)$ where $a$ is half the length of the major axis and $e$ is the eccentricity. So, $$ae =2$$ The distance from the origin to your top is $b$, half the length of the minor axis. $$b=4$$
Squaring the first equation and using the relation $e^2 =1-\frac{b^2}{a^2}$, $$ a^2 -b^2 =4 \implies a^2 =20 $$
The equation of the ellipse is $$\frac{x^2}{a^2} +\frac{y^2}{b^2} =1 \\ \frac{x^2}{20} +\frac{y^2}{16} =1 $$