Question

In the ellipse equation below, what are the coordinates of the foci?

Answer 1

(h+c, k), and (h-c, k)

Answer 2

\(\bf \cfrac{(x-\color{red}{h})^2}{a^2}+\cfrac{(y-k)^2}{b^2}=1\\ \quad \\ \quad \\
\cfrac{(x-7)^2}{625}+\cfrac{(y+3)^2}{225}=1\implies \cfrac{(x-\color{red}{7})^2}{25^2}+\cfrac{(y-(-3))^2}{15^2}=1\\ \quad \\

foci\implies (\color{red}{h\pm c}, k)\qquad \color{red}{c}=\sqrt{a^2-b^2}\)

Answer 3

get the center coordiinates
get the "c" value
add/subtract "c" to the x-coordinate of the center