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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)

Respuesta :

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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