Question

Help with ellipses?

Answer 1

I'm supposed to find the vertices and foci. I'm pretty sure I know how to draw/graph them out just not sure how to get the numbers. The equation I am given is \[16x^2+9y^2=144\]I would like a step by step process if at all possible :)

Answer 2

divide both side by 144 to get 1 from RHS
the leftover at the bottom of x and y form the form of an ellipse
\[\frac{ x^2 }{ a^2 }+\frac{ y^2 }{ b^2 }=1\]
from then you can find out foci, vertices by definition of an ellipse