SOLUTION: find the equation of the parabola with the given focus and directrix. focus (5,-2), directrix y=1
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Question 1162872: find the equation of the parabola with the given focus and directrix. focus (5,-2), directrix y=1
Found 2 solutions by josgarithmetic, greenestamps:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
Use the definition for Parabola based on the Distance Formula.
All points (x,y) equally distant from (5,-2) and (x,1).
, and simplify from here,...
.
.
If no mistakes made done on paper, then .
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!
The focus is below the directrix, so the parabola opens downward. The vertex form of the equation of the parabola is
where (h,k) is the vertex and p is the directed distance from the vertex to the focus.
The vertex is halfway between the focus and the directrix: (5,-.5). That makes p = -1.5.
The equation is
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