Question

The equation of an ellipse is shown.
(x+2)^2/100 + (y+7)^2/36 = 1
What are the coordinates of the foci?

Answer 1

(-10, -7) and (6, -7)
(-6, 7) and (10, 7)
(-2, -15) and (-2, 1)
(2, -1) and (2, 15)

Answer 2

I think it is (-6, 7) and (10, 7)

Answer 3

hmm how did you get (-6, 7) and (10, 7) ?

Answer 4

The translation will be more obvious if you write it as:
\[\frac{(x-(-2))^2}{10^2}+\frac{(y-(-7))^2}{6^2}\]

Answer 5

In general, the centre of an ellipse is translated from the origin (0,0) to (h,k) using:
\[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}\]
where a, b are the horizontal and vertical axes.
and the foci are (h+c, k), (h-c,k) when a>b,
(h,k-c), (h,k+c) when a<b.
also, 2c is the focal distance, where c^2=|a^2-b^2|