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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llltkl | College Teacher | (Level 3) Valedictorian

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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)`
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`

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

This is the required equation.

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