Question

Write an equation of an ellipse centered at the origin with the height 8 units and width 16 units.

Answer 1

well... hm one sec

Answer 2

is centered at the origin... so hmmm


so... now recall that \(\bf \cfrac{(x-{\color{brown}{ h}})^2}{{\color{purple}{ a}}^2}+\cfrac{(y-{\color{blue}{ k}})^2}{{\color{purple}{ b}}^2}=1

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


so.. .what do you think is our "h" and "k" and our "a" and "b" components?

Answer 3

\(\sf\Large \frac{x^2}{\left( \frac{width}{2} \right)^2} + \frac{y^2}{\left(\frac{height}{2}\right)^2}=1\)

Answer 4

If the height was greater than the width, then (height/2)^2 would be under x^2 and (width/2)^2 would be under y^2

Answer 5

@l_o_w_key It would be nice if you could tell us where you are stuck at, or if you have understood what you have been told. :)

Answer 6

(0,16)(8,0)?

Answer 7

forget that. one sec

Answer 8

ahemm ... and so :)

Answer 9

:)

Answer 10

just to clarify
on the graph above, it's wider, and the width runs over the x-axis
thus the "a" component goes below the numerator with the "x" variable