# How do you write an equation of an ellipse in standard form given vertices (6, 0), (-6, 0) and co-vertices (0, 2), (0, -2)?

Oct 26, 2017

The equation of the ellipse is ${x}^{2} + 9 {y}^{2} = 36$

#### Explanation:

Vertices of the Major axis of ellipse are $\left(a , 0\right) , \left(- a , 0\right)$

or $\left(6 , 0\right) , \left(- 6 , 0\right)$ and vertices of the Minor axis of ellipse are

$\left(0 , b\right) , \left(0 , - b\right)$ or $\left(0 , 2\right) , \left(0 , - 2\right)$

Equation of an ellipse with its major axis on the x-axis and minor

axis on the y-axis is: x^2/a^2 + y^2/b^2 = 1 ; a and b are the length

of semi major axis and semi minor axis. Here major axis is

$2 a = 6 + 6 = 12 \therefore a = 6$ and minor axis is

$2 b = 2 + 2 = 4 \therefore b = 2$. Hence the equation of the ellipse is

${x}^{2} / {6}^{2} + {y}^{2} / {2}^{2} = 1 \mathmr{and} {x}^{2} / 36 + {y}^{2} / 4 = 1 \mathmr{and} {x}^{2} + 9 {y}^{2} = 36$ [Ans]