Question

Find the center, vertices, and foci of the ellipse with equation 3x2 + 6y2 = 18
@amistre64 @mathstudent55 help me please

Answer 1

Medal :)

Answer 2

I'm Guessing it's this Center: (0, 0); Vertices: point negative square root of six comma zero and point square root of six comma zero; Foci: Ordered pair negative square root three comma zero and ordered pair square root three comma zero

Answer 3

the center should be obvious

Answer 4

Center: (0, 0); Vertices: point negative square root of six comma zero and point square root of six comma zero; Foci: Ordered pair negative square root three comma zero and ordered pair square root three comma zero
I'm guessing its this

Answer 5

since the center is 0,0 then the vertexes will simply be the solutions for x=0, solve for y .... and y=0, solve for x

Answer 6

foci are trickier, but doable

rewriting the equation into an =1 format we can read the bottoms under the x and y parts

3x2 + 6y2 = 18


3x2 6y2 18
---- + ---- = ----
18 18 18


x2 y2
----- + ----- = 1
18/3 18/6


x2/6 + y2/3 = 1

now the foci are along along the x axis, since under x is larger, the distance is detemrined by some malformed pythagorean thrm:

f^2 + x^2 = 6^2 will determine f for us

Answer 7

last line is a typo

f^2 + 3^2 = 6^2, solves for f

Answer 8

youve guessed at the foci, but we have 4 verts ... 2 you named correctly, and you called the other 2 the foci :)