Question

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

a) (y – 4)² = –12(x – 2)
b) (x – 2)² = –12(y – 4)
c) (y²)² = 12(x²)
d) (x²)² = 4(y⁴)

Answer 1

The equation that represents the parabola is (y – 4)² = –12(x – 2).

Step-by-step explanation:

The equation that represents the parabola with a vertex at (2, 4) and directrix y = 7 can be found using the formula for the equation of a parabola in vertex form, which is (x-h)² = 4p(y-k), where (h, k) is the vertex and p is the distance between the vertex and the directrix. In this case, the vertex is (2, 4) and the directrix is y = 7. The distance between the vertex and the directrix is 4 units, so p = 4. Substituting these values into the equation gives (x-2)² = 4(4)(y-4), which simplifies to (x-2)² = 16(y-4). Therefore, the correct equation is option a) (y – 4)² = –12(x – 2).