# How do you graph \frac { ( x - 3) ^ { 2} } { 9} + \frac { ( y - 5) ^ { 2} } { 25} = 1?

Aug 7, 2018

See the explanation below.

#### Explanation:

This is the equation of an ellipse with a vertical major axis

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

Here, the equation is

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

$a = 5$

$b = 3$

$c = \sqrt{{a}^{2} - {b}^{2}} = \sqrt{25 - 9} = \pm 4$

The center of the ellipse is $C = \left(h , k\right) = \left(3 , 5\right)$

The vertices are

$A = \left(h . k + a\right) = \left(3 , 10\right)$ and $A ' = \left(h , k - a\right) = \left(3 , 0\right)$

And

$B = \left(h + b , k\right) = \left(6 , 5\right)$ and $B ' = \left(h - b , k\right) = \left(0 , 5\right)$

With the vertices, you can graph the ellipse.

graph{((x-3)^2/3^2+(y-5)^2/5^2-1)=0 [-8.84, 19.64, -0.63, 13.61]}