What is the equation of a parabola if the vertex

Question

. What is the equation of a parabola if the vertex is (1, 4) and the directrix is located at y = 3

Answer 1

The equation of a parabola is (x-h)² = 4p(y-k) for a parabola pointing up or down, (y-k)² = 4p(x-h) for a parabola pointing left or right.

The vertex is (h, k) and p is the distance from the vertex to the directrix.

Since the directrix is y = 3, we know the parabola is pointing up or down. It opens up if 4p > 0, and it opens down if 4p < 0.

So we know h = 1, and k = 4.

If the directrix is y = 3, we need to find the distance from vertex to directrix, which is 4 - 3 = 1 = p

Since p = 1, 4p > 0 so this parabola opens up.

(p is also the distance from the vertex to the Focus, Focus = (h, k+p).

Now that we know p, h, and k, we can write the equation of the parabola:

(x-1)² = 4(y-4)

Answer 2

Equation of parabola (x - 1)² = 4p(y - 4), where distance between vertex and directrix is p = 4 - 3 = 1

(x - 1)² = 4(y - 4) is desierd equation of parabola..