Question

Which of the following equations represents the parabola with vertex at (2,4) and directrix y=7

a. (y-4)² = -12 (x - 2)
b. (x - 2)² = -12 (y - 4)
c. (y + 2)² = 12 (x + 2)
d. (x + 2)² = 4 (y + 4)

Answer 1

The equation that represents the parabola with vertex at (2,4) and directrix y=7 is (y-4)² = -12 (x - 2).

Step-by-step explanation:

The equation that represents the parabola with vertex at (2,4) and directrix y=7 is (y-4)² = -12 (x - 2).

To determine this, we can use the standard form of the equation of a parabola, which is (y - k)² = 4a(x - h) where (h, k) is the vertex and a is the distance from the vertex to the focus and directrix.

In this case, the vertex is (2,4), so h = 2 and k = 4. The distance from the vertex to the directrix is 3 units, so a = -3.

Substituting these values into the standard form equation, we get (y - 4)² = -12(x - 2).