How do you find foci of ellipse?

Answer 1

Let's start with the equation of the ellipse.

x2/a2 +y2 /b2 =1

This ellipse is centered at the origin, and we can move it by subtracting h from x and k from y and then squaring that quantity. For example, if we move it h units horizontally, we have (x-h)2 instead of just x2 .

In any case. b2 =a2 -c2 .

The foci are located 2c units part. So if it is centered at the origin, we can just find 2c and each focus is at + or - c.

If we move the ellipse, we can still do the same thing, we just need to take into account how much we moved it.

Here is an example to help you see it.

Vertices (4,0) and (-4,0)

center (0,0)

End points of minor axis (0,2) and (0,-2)

Foci at (3.5,0) and (-3.5,0)