# How do you find the standard form of 3x^2/12+ 5y^2/500 = 1 and what kind of a conic is it?

Jan 4, 2016

An ellipse.

#### Explanation:

Simplify the fractions.

${x}^{2} / 4 + {y}^{2} / 100 = 1$

This fits the mold for an ellipse, which has the general form

${\left(y - k\right)}^{2} / {a}^{2} + {\left(x - h\right)}^{2} / {a}^{2} = 1$

However, the terms at first are switched since $a > b$ for all ellipses, here denoting a vertically oriented ellipse.

Thus, the actual general form is

${y}^{2} / 100 + {x}^{2} / 4 = 1$

Here, $h = 0 , k = 0 , a = 10 , b = 2$.

graph{y^2/100+x^2/4=1 [-22.81, 22.8, -11.4, 11.41]}