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Question 801045: Hi! I have a problem that asks: "Find the focus and directrix of the parabola from the given equation. "
The first problem is: y^2=16x
I tried using this formula: "(y-k)^2=4p (x-h) and only figured out the vertex, which in this case would be (0,0). I don't understand the rest. I tried finding the directrix and focus but I just don't understand how to at all. Please help. Thank you! :)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Find the focus and directrix of the parabola from the given equation. "
The first problem is: y^2=16x
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There are 4 different forms of equation for parabolas with vertices at the origin:
x^2=4py (parabola opens up)
x^2=-4py (parabola opens down)
y^2=4px (parabola opens right)
y^2=-4px (parabola opens left)
..
Equation of given parabola y^2=16x is the 3rd form listed
It is a parabola that opens right with vertex at (0,0)
Its axis of symmetry:y=0 or x-axis
4p=16
p=4
directrix:x=-4 (p-distance to the left of the vertex on the axis of symmetry
focus:(4,0)(p-distance to the right of the vertex on the axis of symmetry
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