# How do you write the equation of an ellipse with vertices at (-5,1) and (-1,1) and co-vertices at (-3,2) and (-3,0)?

Aug 6, 2016

${\left(x + 3\right)}^{2} / 4 + {\left(y - 1\right)}^{2} / 1 = 1$

#### Explanation:

Center (h,k) lies on the x-axis .

so midpoint of vertices is the center.

$\left(h , k\right) = \left(\frac{- 5 + \left(- 1\right)}{2} , \frac{1 + 1}{2}\right) = \left(- 3 , 1\right)$

a=length of semi-major axis $a = 2$
b=length of semi-minor axis$b = 1$

Equation of ellipse:

$\frac{x - h}{a} ^ 2 + \frac{y - k}{b} ^ 2 = 1$

Plug the values of a,b and (h,k)

${\left(x + 3\right)}^{2} / 4 + {\left(y - 1\right)}^{2} / 1 = 1$