# WHAT IS THE EQUATION OF AN ELLIPSE WITH THE FOCI OF (0,4),(0,-4) AND VERTICES (0,8) (0,-8)???

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Student Comments

llltkl | Student

The center is midway between the foci, i.e. at (0, 0).

For a vertical ellipse:

` (y-k)^2/a^2 + (x-h)^2/b^2 = 1 `

center (h, k)

a ≥ b > 0

vertices `(h, k+-a)`

focal distance `c = sqrt(a^2-b^2)`

foci `(h, k+-c)`

For a vertical ellipse:

` (y-k)^2/a^2 + (x-h)^2/b^2 = 1 `

center (h, k)

a ≥ b > 0

vertices `(h, k+-a)`

focal distance `c = sqrt(a^2-b^2)`

foci `(h, k+-c)`

Here,

`h = 0`

`k = 0 `

`a = 8 `

`c = 4 `

`b^2 = a^2- c^2 = 48 `

`(y-0)^2/64 + (x-0)^2/48 = 1`

`h = 0`

`k = 0 `

`a = 8 `

`c = 4 `

`b^2 = a^2- c^2 = 48 `

`(y-0)^2/64 + (x-0)^2/48 = 1`

`rArr y^2/64+x^2/48=1`

This is the required equation.