Question 949612: find the equation of the parabola whose vertex is at (h,k) and satisfying the given conditions. opens upward, length of the latus rectum =8, and passing through (1, 1/2) and (7, -1).
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! find the equation of the parabola whose vertex is at (h,k) and satisfying the given conditions. opens upward, length of the latus rectum =8, and passing through (1, 1/2) and (7, -1).
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basic form of equation for a parabola: (x-h)^2=4p(y-k)
latus rectum=8=4p
equation: (x-h)^2=8(y-k)
2-equations using coordinates of 2 given points (1, 1/2) and (7, -1).
..
(1-h)^2=8(1/2-k)
(7-h)^2=8(-1-k)
..
1-2h+h^2=4-8k
49-14h+h^2=-8-8k
subtract eliminating h^2 and-8k
-48+12h=12
12h=60
h=5
8k=4-1+2h-h^2=3+10-25=-12
k=-12/8=-3/2=-1.5
equation: (x-5)^2=8(y+1.5)
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