# How do you find the standard form given 2x^2+4y^2+12x-8y+25=0?

Feb 14, 2017

This is an invalid equation. It represents an imaginary ellipse, with imaginary semi axes $a = i \sqrt{3} \mathmr{and} b = i \frac{\sqrt{3}}{2}$.

$i \sqrt{3}$.

#### Explanation:

In the standard form, the equation is

$\left(2 {\left(x + 3\right)}^{2} - 18\right) + \left(4 {\left(y - 1\right)}^{2} = 4\right) + 25 = 0$, giving

$2 {\left(x + 3\right)}^{2} + {\left(y - 1\right)}^{2} + 3 = 0$,