Question

PLEASE HELP WILL GIVE A MEDAL
Find an equation in standard form for the ellipse with the vertical major axis of length 16, and minor axis of length 10.

Answer 1

@DanJS

Answer 2

@jdoe0001

Answer 3

vertical MAJOR axis is 16, so that means that
the equation with the "y" variable, will have the "bigger" denominator, or "a" component

so... we dunno the coordinates, it's saying in "standard form" so, the assumption is the center is 0,0 or the origin
thus \(\bf \cfrac{(x-{\color{brown}{ h}})^2}{{\color{purple}{ b}}^2}+\cfrac{(y-{\color{blue}{ k}})^2}{{\color{purple}{ a}}^2}=1

\qquad center\ ({\color{brown}{ h}},{\color{blue}{ k}})\qquad
vertices\ ({\color{brown}{ h}}, {\color{blue}{ k}}\pm a)\)

plug and chug