Question

Rosa is constructing a parabola on a coordinate plane. Derive the equation of the parabola she’s drafting, with a focus at (−2,1)
and a directrix at y=−1
.(1 point)
Responses

y=14x2+x+4
y equals Start Fraction 1 over 4 End Fraction x squared plus x plus 4

y=−14x2+2x−6
y equals negative Start Fraction 1 over 4 End Fraction x squared plus 2 x minus 6

y=−14x2+x+4
y equals negative Start Fraction 1 over 4 End Fraction x squared plus x plus 4

y=14x2+x+1

Answer 1

Use the distance definition: for any point (x,y),
sqrt[(x+2)^2+(y-1)^2] = distance to directrix = |y+1|.
Square both sides:
(x+2)^2+(y-1)^2 = (y+1)^2
(x+2)^2 -2y = 2y
(x+2)^2 = 4y
y = 1/4 (x+2)^2 = (1/4)x^2 + x + 1.

So the correct choice is y = (1/4)x^2 + x + 1 (the last option).