Question

Someone please help ! I don't understand how to do this . What is the equation of the ellipse with co-vertices (0, 2), (0, -2) and vertices (3, 0), (-3, 0)?

Answer 1

well, have you done ellipses yet?

Answer 2

Yes , but I forgot how to do them ..

Answer 3

let's take a peek at the vertices, they're at (3, 0), (-3, 0)
notice the "y" didn't change
the "x" did, that means is horizontal or of horizontal major axis
over the x-axis it goes from 3 to -3, how long is that? well 6 units
"a" component is half-that, so
a = 3

the "co-vertices" or the vertices for the minor axis are (0, 2), (0, -2)
if our major axis is horizontally oriented, our minor axis will be vertically oriented,
notice the "x" didn't change, the "y" did, went from 2 to -2, that is 4 units
half that is the "b" component
b = 2

what about the center?

Answer 4

the center is half-way between the vertices of either axis
let's use the major, the major axis vertices are at (3, 0), (-3, 0)
let's use the midpoint for that \(\bf \left(\cfrac{x_2 + x_1}{2},\cfrac{y_2 + y_1}{2} \right)\\
\left(\cfrac{3 + -3}{2},\cfrac{0 + 0}{2} \right) \implies (0, 0)\)

Answer 5

Wouldn't the center be at (0,0) ?

Answer 6

yes :)

Answer 7

Yay ! (:

Answer 8

Thank you for your help . (: