Find the equation of the ellipse with x intercepts at (±6, 0) and y intercepts at (0,±4) and find the foci.
The vertices are marked with V's, the foci with F's
Ellipses which have this shape (like an egg sitting on a table,
not like the number "0") have this equation (learn it):
The green line is a, which is 6 units long, called the semi-major axis
The purple line is b, which is 4 units long, called the semi-minor axis,
so the equation of the ellipse is
or
The foci (±c,0) are found by this Pythagorean equation for all ellipses:
The foci are and
Edwin
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