Find the equation of the parabola with its focus at (3,4) and its directrix y = 0.

Equation of parabola: 8 * (y - 2) = (x - 3) ^2

or

y = (1/8) * (x - 3) ^2 + 2

Step-by-step explanation:

focus at (3,4) and its directrix y = 0.

Focus equation: (h, k + c) = (3, 4)

Directrix equation y = k - c = 0

so h = 3, k + c = 4, k - c = 0

Solve the system : k + c = 4 and k - c = 0

add the equations together: k + c + k - c = 4 + 0

2k = 4

k = 2

so k + c = 4, 2 + c = 4, c = 2

4c (y - k) = (x - h) ^2

4*2 * (y - 2) = (x - 3) ^2

8 * (y - 2) = (x - 3) ^2