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Question 95261: When given the coordinates (3,8) how do you know which number is substituted when solving for (h and k) for the focus and the directrix for parabolas.
The Problem
1. Write an equation for a parabola with focus (3,8) and a directrix y = 4.
Focus: (h, k+ 1/4a) (h + 1/4a, k)
Directrix: y = k-1/4a x = h -1/4a
Can you try and explain it as thoroughly as possible, so I can understand it? The online course I am doing doesn't explain how to be from point a to point b.
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! When given the coordinates (3,8) how do you know which number is substituted when solving for (h and k) for the focus and the directrix for parabolas.
The Problem
1. Write an equation for a parabola with focus (3,8) and a directrix y = 4.
Focus: (h, k+ 1/4a) (h + 1/4a, k)
Directrix: y = k-1/4a x = h -1/4a
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1st: Plot the point (3,8) and draw the line y=4 so you can see what I'm
talking about.
2nd: The vertex is half way between (3,8) and the line y=4; so the
coordinates of the vertex are x=3 and y=6
Note: Those are the values of h and k; h=3 and k=6
3rd: The distance of the focus from the vertex = 8-6=2 is the value of p
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Parabola form:
(x-h)^2 = 4p(y-k)
(x-3)^2 = 8(y-6)
y-6 = (1/8)(x-3)^2
y = (1/8)(x-3)^2+6
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Cheers,
Stan H.
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