Question

Find the parabola with focus (9,7) and directrix x = -10.

a) (x - 9)² = 4
b) (x + 9)² = 4
c) (x - 9)² = -4
d) (x + 9)² = -4

Answer 1

The parabola with focus (9,7) and directrix x = -10 is represented by the equation (x - 9)² = 76(y - 7).

Step-by-step explanation:

The parabola can be found using the formula (x - h)² = 4p(y - k), where (h, k) is the coordinates of the vertex and p is the distance from the vertex to the focus or directrix. In this case, the focus is (9,7), so the vertex is (9,7 - p).

The parabola with focus (9,7) and directrix x = -10 is represented by the equation (x - 9)² = 76(y - 7).

The directrix is x = -10, so the vertex is (-10 + p, 7). Equating the x-coordinates of the vertex, we get 9 = -10 + p, so p = 19. Substituting the values into the formula, we get (x - 9)² = 4(19)(y - 7), which simplifies to (x - 9)² = 76(y - 7).