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7 March, 20:21

Find the center, vertices, and foci for the ellipse 25x^2+64y^2=1600

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Answers (2)
  1. 7 March, 20:38
    0
    Step-by-step explanation:

    Answer:

    Data

    Equation 25x² + 64y² = 1600

    Process

    1. - Divide all the equation by 1600

    25x²/1600 + 64y² / 1600 = 1600/1600

    -Simplify

    x²/64 + y² / 25 = 1

    2. - Equation of a horizontal ellipse

    3. - Find a, b and c

    a² = 64 a = 8

    b² = 25 b = 5

    -Calculate c with the Pythagorean theorem

    a² = b² + c²

    -Solve for c

    c² = a² - b²

    -Substitution

    c² = 8² - 5²

    -Simplification

    c² = 64 - 25

    c² = 39

    -Result

    c = √13

    4. - Find the center

    C = (0, 0)

    5. - Find the vertices

    V1 = (-8, 0) V2 = (8, 0)

    6. - Find the foci

    F1 = (-√13, 0) F2 = (√13, 0)
  2. 7 March, 20:48
    0
    Answer: A

    Step-by-step explanation: Center (0,0)

    Vertices (+/-8,0)

    Foci (+/-6.2,0)
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