# How do you write an equation of an ellipse given endpoints of major axis at (2,12) and (2,-4) and endpoints of the minor axis at (4,4) and (0,4)?

Apr 29, 2017

The equation is ${\left(y - 4\right)}^{2} / 64 + {\left(x - 2\right)}^{2} / 4 = 1$

#### Explanation:

The equation of an ellipse with a vertical major axis is

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

The length of the major axis is $a = \frac{12 - \left(- 4\right)}{2} = 8$

The length of the minor axis is $b = \frac{4 - 0}{2} = 2$

The center of the ellipse is $\left(h , k\right) = \left(2 , 4\right)$

The equation of the ellipse is

${\left(y - 4\right)}^{2} / 64 + {\left(x - 2\right)}^{2} / 4 = 1$

graph{(y-4)^2/64+(x-2)^2/4=1 [-28.65, 29.11, -14.68, 14.2]}