# How do you find the coordinates of the center, foci, the length of the major and minor axis given x^2/25+y^2/9=1?

Nov 14, 2016

#### Explanation:

The standard form for an ellipse is:

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

The centerpoint is:

$\left(h , k\right)$

The vertices are at:

$\left(h - a , k\right) , \left(h + a , k\right) , \left(h , k - b\right) , \mathmr{and} \left(h , k + b\right)$

If $a > b$ then the foci are at:

$\left(h - \sqrt{{a}^{2} - {b}^{2}} , k\right) \mathmr{and} \left(h + \sqrt{{a}^{2} - {b}^{2}} , k\right)$

The length of the major axis is $2 a$

The length of the minor axis is $2 b$

If $b > a$ then the foci are at:

$\left(h , k - \sqrt{{b}^{2} - {a}^{2}}\right) \mathmr{and} \left(h , k + \sqrt{{b}^{2} - {a}^{2}}\right)$

The length of the major axis is $2 b$

The length of the minor axis is $2 a$

Convert the given equation to standard form:

${\left(x - 0\right)}^{2} / {5}^{2} + {\left(y - 0\right)}^{2} / {3}^{2} = 1$

The centerpoint is:

$\left(0 , 0\right)$

The vertices are at:

$\left(- 5 , 0\right) , \left(5 , 0\right) , \left(0 , - 3\right) , \mathmr{and} \left(0 , 3\right)$

$a > b$ then the foci are at:

$\left(- 4 , 0\right) \mathmr{and} \left(4 , 0\right)$

The length of the major axis is $10$

The length of the minor axis is $6$