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=18x2−54x+178

y=−18x2−2x+1

y=−18x2−54x+38

y=18x2−34x+18

Answer 1

Use the definition: distance to focus = distance to directrix.

For (x,y), sqrt((x−3)^2 + (y−1)^2) = |y + 3|. Square and simplify:
(x−3)^2 + (y−1)^2 = (y+3)^2
(x−3)^2 − 2y + 1 = 6y + 9
(x−3)^2 = 8(y + 1)

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

None of the four multiple-choice options match this equation.