Write the equation for a parabola with the focus at (–1, 4) and the equation of the directrix x = 5.
Accepted Solution
A:
A standard form of the equation of a rotated parabola is (y - k)² = 4p(x - h) where (h, k) is the location of the vertex. (h+p, k) is the location of the focus. The directrix is the line x = h - p
Because the focus is at (-1, 4), therefore h + p = -1 (1) k = 4 (2)
Because the directrix is x = 5, therefore h - p = 5 (3)
Add equations(1) and (3) to obtain h + p + (h - p) = -1 + 5 2h = 4 h = 2 From (1), obtain p = -1 - h = -1 - 2 = -3
The equation of the parabola is (y - 4)² = -12(x - 2)