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Question 450434: If given the equation of a parabola, how do i find the focus?
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! If given the equation of a parabola, how do i find the focus?
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There are 4 basic equations for the parabola from which you can find the focus as follows:
1) x^2=4py (parabola opens upwards, axis of symmetry vertical)
2) x^2=-4py (parabola opens downwards, axis of symmetry vertical)
3) y^2=4px (parabola opens rightwards, axis of symmetry horizontal)
4) y^2=-4px (parabola opens leftwards, axis of symmetry horizontal)
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In all four cases, if you find p, you can find the focus. 4p is the coefficient of x or y as the case might be. p is also the distance from vertex to focus and from vertex to directrix on the axis of symmetry. If you know 2 out of the 3 items( p, vertex, and directrix) you should be able to find the focus.
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