Question

Demetrius is drafting a parabola on a coordinate plane. He plans to have the focus at (3,1)
and the directrix at y=−3
. What is the equation in standard form that represents the parabola?(1 point)

y=18x2−34x+18


y=−18x2−54x+38


y=−18x2−2x+1


y=18x2−54x+178

Answer 1

Focus (3,1) and directrix y = −3 give vertex at midpoint (3,−1) and p = 2. So (x−3)^2 = 4p(y+1) = 8(y+1).

Thus y = (x−3)^2/8 − 1 = (1/8)x^2 − (3/4)x + 1/8.

None of the four given choices match this equation.