Question

Find the equation of the parabola with its focus at (6,2) and its directrix y = 0.
A) y = -1/4(x - 6)² + 1

Answer 1

The equation of the parabola with its focus at (6,2) and its directrix y = 0, is determined as y = 1/4(x - 6)² + 1.

Equation of the parabola

Focus at (6,2) and its directrix y = 0.

Focus equation is given as:  (h, k + c) = (6, 2)

Directrix equation is given as:   y =  k - c = 0

so  h = 6,   k + c = 2,   k - c = 0

Solve  the system :  k + c = 2 and k - c = 0

add the equations together:     k + c + k - c = 2 + 0

2k = 2

k = 1

so   k + c = 2,    

1 + c = 2  

c = 1

4c (y - k) = (x -  h)²

4(1)(y - 1) = (x - 6)²

4(y - 1) = (x - 6)²

4y - 4 = (x - 6)²

4y = (x - 6)² + 4

y = 1/4(x - 6)² + 1

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