# How do you write an equation for an ellipse given endpoints of the major axis at (0,10) and (0,-10) and foci at (0,8) and (0,-8)?

Jan 9, 2018

The equation of ellipse is ${x}^{2} / 36 + {y}^{2} / 100 = 1$

#### Explanation:

Semi major axis is $a = 10$ and focus $c = 8$ from the centre

$\left(0 , 0\right)$ . This is vertical ellipes of which the equation is

${x}^{2} / {b}^{2} + {y}^{2} / {a}^{2} = 1 \mathmr{and} {x}^{2} / {b}^{2} + {y}^{2} / {10}^{2} = 1$

c is the distance from the center to a focus. The relation of

$c , a , b$ is ${c}^{2} = {a}^{2} - {b}^{2} \therefore {8}^{2} = {10}^{2} - {b}^{2}$ or

${b}^{2} = 100 - 64 = 36 : b = 6$

Hence the equation of ellipse is ${x}^{2} / {6}^{2} + {y}^{2} / {10}^{2} = 1$ or

${x}^{2} / 36 + {y}^{2} / 100 = 1$

graph{(x^2/36+y^2/100)=1 [-40, 40, -20, 20]} [Ans]