Question

Find the vertices and foci of the hyperbola with equation ((x + 4^2)/ 9) - ((y - 5^2) /16) = 1.

Answer 1

You mean,
\[((x + 4)^2/ 9) - ((y - 5)^2 /16) = 1\] That can be expressed,
\[((x - (- 4))^2/ 3^2) - ((y - 5)^2 /4^2) = 1\]
With this you have a=3, b=4, and can obtain the foci with,
\[c=\pm\sqrt{b^2+a^2}\]