# How do you write an equation of an ellipse given the major axis is 16 units long and parallel to the x axis, minor axis 9 units long, center (5,4)?

Dec 13, 2017

${\left(x - 5\right)}^{2} / 64 + \frac{4 {\left(y - 4\right)}^{2}}{81} = 1$

#### Explanation:

The equation of an ellipse given its major axis as $2 a$ parallel to the $x$-axis, minor axis $2 b$ units long, obviusly parallels to $y$-axis and center $\left(h , k\right)$ is

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

Here we have major axis $16$ and hence $2 a = 16$ or $a = 8$ and minor axis is $2 b = 9$ or $b = \frac{9}{2}$. As center is $\left(5 , 4\right)$, the equation of ellipse is

${\left(x - 5\right)}^{2} / {8}^{2} + {\left(y - 4\right)}^{2} / {\left(\frac{9}{2}\right)}^{2} = 1$

or ${\left(x - 5\right)}^{2} / 64 + \frac{4 {\left(y - 4\right)}^{2}}{81} = 1$

graph{ (x-5)^2/8^2+(y-4)^2/(9/2)^2=1 [-5, 15, -1, 9]}