Question 968532: Write the equation of the directix of the conic section shown below:
y^2-4x+4y-4=0
(please help, thank you)
Answer by josgarithmetic(39620)   (Show Source):
You can put this solution on YOUR website! Skipping the fundamental derivation, but for directrix (-p,y) using p as a positive number, focus (p,0), for parabola in standard form a axis of symmetry being the x-axis, equation is  . If vertex were some point (h,k), then the equation of this parabola is  .
Your example problem equation is easily transformed into  . You can make the correspondances to find p=1 IF you had parabola in standard form and standard position, but your case is that vertex is pushed to the left by 2 units. See, your vertex is (-2,-2); your directrix is  , or simply now  .
Remember, p was taken as nonnegative in the fundamental derivation for standard position, so directrix is p units to the left of the vertex point, and vertex would be on the origin.
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