Question

Which of the following equations represents the parabola with vertex at (4, 1) and directrix y = 6?
O(y-1)2 = -8(x-4)
O(y + 1)² = 8(x + 4)
O(x-4)² = -20(y-1)
O(x+4)² = 20(y + 1)

Answers

  1. The equation that represents the parabola with vertex at (4, 1) and directrix y = 6 is; D: (x – 4)² = -20(y – 1)

    What is the equation of the parabola?

    If a parabola has a vertical axis, the standard form of the equation of the parabola is this: (x – h)² = 4p(y – k)
    where p≠ 0.
    The vertex of this parabola is at (h, k). The focus is at (h, k + p). The directrix is the line y = k – p.
    We are told that the vertex is at (4, 1). Thus;
    h = 4 and k = 1
    Since y = 6, then we have;
    6 = 1 – p
    p = 1 – 6.
    p = -5
    Thus, equation of parabola is;
    (x – 4)² = 4(-5)(y – 1)
    ⇒ (x – 4)² = -20(y – 1)
    Read more about Equation of Parabola at; https://brainly.com/question/4061870
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