Question

Find an equation in standard form for the ellipse with the vertical major axis of length 18, and minor axis of length 10.

Answer 1

HI!!

Answer 2

centered at the origin?

Answer 3

I think so

Answer 4

major axis of 18, is vertical, thus the vertical is the longest axis
meaning the "a" component goes under the "y"
thus \(\bf \cfrac{(x-{\color{brown}{ h}})^2}{{\color{purple}{ b}}^2}+\cfrac{(y-{\color{blue}{ k}})^2}{{\color{purple}{ a}}^2}=1

\quad center\ ({\color{brown}{ 0}},{\color{blue}{ 0}})\quad
\cfrac{(x-{\color{brown}{ 0}})^2}{{\color{purple}{ 10}}^2}+\cfrac{(y-{\color{blue}{ 0}})^2}{{\color{purple}{ 18}}^2}=1
\\ \quad \\
\cfrac{x^2}{100}+\cfrac{y^2}{324}=1\)

Answer 5

hmmm actually...,

Answer 6

if the vertical axis is ... lemme draw it up

Answer 7

thus that means that the "a" component is 9 and "b" is 5

Answer 8

\(\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}{ 0}},{\color{blue}{ 0}})\implies
\cfrac{(x-{\color{brown}{ 0}})^2}{{\color{purple}{ 5}}^2}+\cfrac{(y-{\color{blue}{ 0}})^2}{{\color{purple}{ 9}}^2}=1
\\ \quad \\
\cfrac{x^2}{25}+\cfrac{y^2}{81}=1\)