Question 832240
How do you find the P and the directrix of the equation of a parabola with its focus on (4,-2) and a vertex of (4,-4)?
how do you find P if vertex is at (2,1) and the directrix is at x = -2? 
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In the first case, parabola opens upward.
Its basic equation: (x+h)^2=4p(y-k)
(x-4)^2=4p(y+4)
axis of symmetry: x=4
focus: (4,-2)
p=2 (distance(-2 to -4) from focus to vertex on the axis of symmetry)
directrix: y=-6
..
In the 2nd case, parabola opens rightward. 
axis of symmetry: y=1
p=4 (distance(-2 to 2) from directrix to vertex on the axis of symmetry)
focus: (6,1)