Answer:
B
Step-by-step explanation:
Given focus as (h,k) and directrix as y = mx + b, the equation of a parabola is given as:
[tex]\frac{(y - mx - b)^2}{m^2 +1}=(x - h)^2 + (y - k)^2[/tex]
Hence, from the given focus & directrix, we have:
h = -1
k = -1
m = 0
b = 1
We can plug them into the formula and arrange to get:
[tex]\frac{(y - mx - b)^2}{m^2 +1}=(x - h)^2 + (y - k)^2\\\frac{(y - (0)x - 1)^2}{0^2 +1}=(x - (-1))^2 + (y - (-1))^2\\\frac{(y-1)^2}{1}=(x+1)^2+(y+1)^2\\y^2-2y+1=x^2+2x+1+y^2+2y+1\\-2y-2y=x^2+2x+1\\-4y=x^2+2x+1\\y=-\frac{1}{4}x^2-\frac{1}{2}x-\frac{1}{4}[/tex]
B is the correct answer.
