Question

Write an equation for an ellipse centered at the origin, which has foci at ( 0 , ± 24 ) (0,±24)left parenthesis, 0, comma, plus minus, 24, right parenthesis and co-vertices at ( ± 10 , 0 ) (±10,0)

Answer 1

x^2/100+y^2/676=1

Explanation:

Answer 2

`(x^(2))/(400) + (y^(2))/(976) = 1`

Explanation:

The distance between foci with respect to origin is determined by mean of the Pythagorean Theorem:

`2\cdot c = \sqrt{(0-0)^(2)+[24-(-24)]^(2)}`

`2\cdot c = 48`

`c = 24`

The distance between origin and any of the horizontal co-vertices is:

`a = \sqrt{[10-(-10)]^(2)+(0-0)^(2)}`

`a = 20`

Now, the distance between origin and any of the vertical co-vertices is determined by the following Pythagorean relationship:

`c^(2) = b^(2) - a^(2)`

`b^(2) = a^(2) + c^(2)`

`b = \sqrt{a^(2)+c^(2)}`

`b = \sqrt{20^(2)+ 24^(2)}`

`b = 4√(61)`

Lastly, the equation of the ellipse in standard form is:

`(x^(2))/(400) + (y^(2))/(976) = 1`