Question

Find the center, vertices, and foci of the ellipse with equation 5x2 + 9y2 = 45.

Answer 1

@misty1212

Answer 2

HI again

Answer 3

first divide by \(45\) to make it in standard form as
\[\frac{x^2}{9}+\frac{y^2}{5}=1\]

Answer 4

is it obvious that the center is \((0,0)\)?

Answer 5

okay and is the 9=a or 9=a^2?

Answer 6

and yes, the center is (0,0)

Answer 7

it is \(a=3\) and since the larger number is under the x, not the y , it looks like the one on the left

Answer 8

that means the vertices are 3 units to the LEFT and RIGHT of the center

Answer 9

again it is important to know what it looks like
so the vertices are \((-3,0)\) adn \((3,0)\)

Answer 10

okay! and then the foci would be (-2,0) and (2,0) right?

Answer 11

\[\color\magenta\heartsuit\]

Answer 12

i.e. yes!

Answer 13

okay cool thank you! i have two more questions hopefully you can help?

Answer 14

kk