Question 11.3.1: Finding an Equation of an Ellipse Find the standard form of ...

Because the foci are (-4, 0) and (4, 0), the major axis is on the x-axis.We know that c = 4 and a = 5. Next find b²:

b^{2}=a^{2}-c^{2}              Relationship between a, b, and c

b^{2}=(5)^{2}-(4)^{2}=9                  Replace c with 4 and a with 5.

Substituting 25 for a^{2} \text { and } 9 \text { for } b^{2} in the standard form for a horizontal ellipse, we get

\frac{x^{2}}{25}+\frac{y^{2}}{9}=1.