# How do you find the coordinates of the center, foci, the length of the major and minor axis given 36x^2+81y^2=2916?

Oct 15, 2016

You can obtain your answers by doing steps 1 through 4 in the explanation.

#### Explanation:

Let divide by 2916 and write the denominators as squares:

${x}^{2} / {9}^{2} + {y}^{2} / {6}^{2} = 1$

When the denominator of the x term is greater than the denominator of the y term, the standard form is:

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

where:

1. $\left(h , k\right)$ is the center point
2. $2 a$ is the length of the major axis
3. $2 b$ is the length of the minor axis
4. The foci are at $\left(h + \sqrt{{a}^{2} - {b}^{2}} , k\right)$ and $\left(h - \sqrt{{a}^{2} - {b}^{2}} , k\right)$

Subtract zero from x and y to put the equation in standard form:

${\left(x - 0\right)}^{2} / {9}^{2} + {\left(y - 0\right)}^{2} / {6}^{2} = 1$