Question 403685: find the equation of a parabola given 2 points on the parabola, (5,9)&(1,9), and the directrix d:y=-1 .
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find the equation of a parabola given 2 points on the parabola, (5,9)&(1,9), and the directrix d:y=-1
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since the directrix=-1, the parabola opens upward.
The standard form of a parabola is, y=(x-h)^2+k, (h,k) being the coordinates of the vertex. Based on the given points,(5,9) and (1,9), the axis of symmetry is between x=1 and x=5, which places it at x=3, the x coordinate of the vertex. The y-coordinate is somewhere on this line.
Using either of the given points,
y=(x-h)^2+k
9=(5-3)^2+k
9=2^2+k
k=5
equation of the parabola: y=(x-3)^2+5
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