A parabola with focus of (3, 4) and a directrix of y = 0 has the equation of the parabola as
<h3>How to write the equation of parabola </h3>
Quadratic equation is equal to parabolic equation, when the directrix is at y direction is of the form:
(x - h)² = 4P (y - k)
OR
standard vertex form, y = a(x - h)² + k
where a = 1/4p
The focus
F (h, k + p) = (3, 4)
h = 3
k + p = 4
P in this problem, is the midpoint between the focus and the directrix
P = (4 - 0) / 2 = 2
p = 2
the vertex
v(h, k)
h = 3
k + p = 4, k = 2
v(h, k) = v(3, 2)
substitution of the values into the equation gives
(x - h)² = 4P (y - k)
(x - 3)² = 4 * 2 (y - 2)
(x - 3)² = 8 (y - 2)
y = 1/8(x - 3)² + 2
The quadratic equation is of the form y = 1/8(x - 3)² + 2
Learn more about vertex of quadratic equations at:
brainly.com/question/29244327
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