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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)?
I tried solving for P but I don't know if it's correct. Here's my solution for P:
Since focus is (h + P, k) in terms of y or (h, P + k)in terms of x, I don't know if the equation is in terms of y or x, so I just made a guess, so: (4 + P, -4); P=-4 or (4, P - 4); P=4?
And also, how do you find P if vertex is at (2,1) and the directrix is at x = -2?
I'm really confused in finding for P but I understand how the basics work in conic sections. Your help will be really appreciated.
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! 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)
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