ellipse has an equation of x^2+3y^2+16x+4=100y? standard form

Answer 1

try completing the squares:

x^2+16x + 3y^2-100y = -4
x^2+16x+64 + 3(y^2 - 100/3y + (50/3)^2) = -4 + 64 + 3*(50/3)^2
(x+8)^2 + (y - 50/3)^2 = 2680/3

unusual, but hey, it's just numbers, right?

But still, it's so odd that I suspect a typo. You sure it's not 4y^2? If so, I'm sure now you can see how to fix it.

Answer 2

oops. I botched it a bit, and lost the 3. We pick it up here:

(x+8)^2 + 3(y - 50/3)^2 = 2680/3
now get rid of that pesky 3:

(x+8)^2/3 + (y-50/3)^2 = 2680/9