Which are the foci of the ellipse represented by 16x^2 + 25y^2 = 400? (–3, 0) and (3, 0) (–5, 0) and (5, 0)

Which are the foci of the ellipse represented by 16x^2 + 25y^2 = 400?

(–3, 0) and (3, 0)
(–5, 0) and (5, 0)
(0, 3) and (0, –3)
(0, 5) and (0, –5)

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  1. The foci of the elipse that has equation 16x² + 25y² = 400 is given as follows:
    (–3, 0) and (3, 0).

    How to obtain the foci of the elipse?

    The equation of the elipse is given as follows:
    16x² + 25y² = 400.
    In standard format, the equation is given by:
    16x²/400 + 25y²/400 = 1.
    x²/25 + y²/16 = 1.
    Hence the coefficients of the equation are given as follows:
    • a² = 25 -> a = 5.
    • b² = 16 -> b = 4.
    This is a vertical elipse, as the highest denominator is with the x-coordinate, and the center is of (0,0), hence the coordinates of the foci are given as follows:
    (c,0) and (-c,0).
    The coefficient c is obtained as follows:
    c² = a² – b².
    Hence:
    c² = 25 – 16
    c² = 9
    c = 3.
    Hence the first option is correct.
    More can be learned about the equation of an elipse at https://brainly.com/question/16904744
    #SPJ1

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