Given that the focus is (-3,-5/4) and the directrix is y= -3/4, what is the equation of the parabola?

Answer 1

We have vertical parabola: (x - h)² = 4p(y-k), (h, k) is vertex.

2p = - 5/4 - (- 3/4) = - 1/2; p = - 1/4. Now vertex is (-3, - 5/4 + 1/4) = (- 3, - 1).

Atlast we get equation: (x + 3)² = 4(- 1/4)(y + 1), or (x + 3)² = - (y + 1)

Answer 2

focus: (h, k + p), k + p = -5/4

directrix: y = k - p, k - p = -3/4

k + p = -5/4

k - p = -3/4

2p = -2/4

p = -1/4

k = -1

h = -3

a = 1 / 4p

a = -4

f(x) = -4(x + 3)² - 1