Question

find the center, foci, and vertices of the ellipse.
(x-4)^2 +9(y+1)^2=36
don't know how to put it in the the basic form

Answer 1

divide both sides of the equation (all terms) by 9

Answer 2

so it will look like (x-4)^2/9 + (y+1)^2 = 4

Answer 3

oops, we want a 1 on the right side, so we should divide both sides by 36 (not 9)

Answer 4

that will give a^2= 36 and b^2= 4

Answer 5

so it will look like (x-4)^2/36 + (x+1)^2/4 =1

Answer 6

yes, that is standard form (except you mean (y+1)^2/4 right?)
center will be at (4,-1)

Answer 7

yes!

Answer 8

focus is "f" away from the center
f= sqrt(a^2-b^2)
see http://en.wikipedia.org/wiki/Ellipse#Equations

Answer 9

so the vertex are (10,-1) and (-2,-1)