Ask Me Help Desk - Ellipses 2y^2+5x^2+12y-20x+10=-18

Yes. And do what?

Write it in the form, $\frac{(x-h)^{2}}{a^{2}}+\frac{(y-k)^{2}}{b^{2}}=1$

If so, complete the square on x and y.

$2y^{2}+12y+5x^{2}-20x=-28$

Complete square:

$5(x^{2}-4x+4)+2(y^{2}+6y+9)=10$

$5(x-2)^{2}+2(y+3)^{2}=10$

Divide by 10:

$\frac{(x-2)^{2}}{2}+\frac{(y+3)^{2}}{5}=1$

The ellipse has center (2,-3), Minor axis length $\sqrt{2}$ and major axis length $\sqrt{5}$