Question

write the standard form of equation of a parabola whose vertex is at (2, 3) and has a directrix at X= 5

Answer 1

`(y-3)^2=-12(x-2)`

Explanation:

'p' is the distance between the vertex and the directrix, so for a parabola with a vertical axis, it opens upward if 'p' is positive and downward if 'p' is negative. Since the vertex of the parabola is at (2, 3) and the directrix is at x=5, the parabola opens to the left. The distance between the vertex and the directrix is 3 units (5 - 2 = 3), so ∣p∣=3.