Question

Write the equation of the parabola
1.Vertex(2,5) Focus(2,-3)
2.Directrix=x=3/4 Focus(5/4,-3)

For 1. i got(x-2)^2=32(y-5)^2
For 2. i got y=8x^2-20x-61/60

Answer 1

1. V(2,5), F(2,-3).
1/4a = -3-5 = -8.
4a = -1/8.
a = -1/32.

Y = a(x-h)^2 + k.
Y = (-1/32)(x-2)^2 + 5, Vertex Form

Answer 2

2. D(3/4,-3), V(h,-3), F(5/4,-3).

1/2a = 5/4-3/4 = 2/4 = 1/2.
2a = 2, a = 1.

1/4a = 1/(4*1) = 1/4.

h = 3/4 + 1/4a = 3/4 + 1/4 = 4/4 = 1.

X = a(y-k)^2 + h.
X = (y+3)^2 + 1, Vertex form.

X = y^2 + 6y + 10, Standard form.