Anonymous
Anonymous asked in Science & MathematicsMathematics · 3 weeks ago

Find an equation for the ellipse that satisfies the given conditions.?

Find an equation for the ellipse that satisfies the given conditions.

Foci: F(0, ±4), vertices: (0, ±5)

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    So it's centered at (0 , 0), obviously

    (x - 0)^2 / a^2 + (y - 0)^2 / b^2 = 1

    x^2 / a^2 + y^2 / b^2 = 1

    We know that it passes through (0 , -5) and (0 , 5)

    0^2 / a^2 + (+/- 5)^2 / b^2 = 1

    25/b^2 = 1

    25 = b^2

    5 = b

    x^2 / a^2 + y^2 / 25 = 1

    F = sqrt(25 - a^2)

    F = 4

    4 = sqrt(25 - a^2)

    16 = 25 - a^2

    a^2 = 9

    a = 3

    x^2 / 9 + y^2 / 25 = 1

    25x^2 + 9x^2 = 225

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