# Thread: Finding the coordinates of foci in an ellipse

1. ## Finding the coordinates of foci in an ellipse

In the following I determined the value of a to be 6 but I can't find the value of b and therefore cannot find the value of c:

"Find the coordinates of the foci of an ellipse centred at the origin, whose vertices have the coordinates: (8, 0) and (0, -4)."

Any help would be greatly appreciated!

2. Hello, s3a!

In the following I determined the value of $\displaystyle a$ to be 6 . How?
but I can't find the value of $\displaystyle b$ .
Really?
and therefore cannot find the value of $\displaystyle c.$

Find the coordinates of the foci of an ellipse centred at the origin,
whose vertices have the coordinates: (8, 0) and (0, -4).
I don't understand what you were taught . . .

The center is at the origin: $\displaystyle (0,0)$
. . So the vertices are at: .$\displaystyle (\pm8,0)\,\text{ and }\,(0,\pm4)$

This tell us immediately that: .$\displaystyle a = 8,\;b = 4$

And $\displaystyle c$ is given by: .$\displaystyle c^2 \:=\:a^2-b^2$