Question

Please help:

Answer 1

A parabola with focus of (3, 4) and a directrix of y = 0 has the equation of the parabola as

• y = 1/8(x - 3)²  + 2

How to write the equation of parabola

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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