SOLUTION: opens upward, end points of the latus rectum at (9,3) and (-7,3). find the equation of the parabola whose vertex is at (h,k).

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: opens upward, end points of the latus rectum at (9,3) and (-7,3). find the equation of the parabola whose vertex is at (h,k).      Log On


   

Question 949613: opens upward, end points of the latus rectum at (9,3) and (-7,3). find the equation of the parabola whose vertex is at (h,k).
Answer by lwsshak3(11628) About Me  (Show Source):
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opens upward, end points of the latus rectum at (9,3) and (-7,3). find the equation of the parabola whose vertex is at (h,k).
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Basic form of equation for given parabola: (x-h)^2=4p(y-k)
x-coordinate of vertex=midpoint between x=9 and x=-3
(9+(-7))/2=2/2=1
h=1
length of latus rectum=9-(-7)=16=4p
solve for k:
(9-1)^2=16(3-k)
64=16(3-k)
3-k=4
k=-1
equation:(x-1)^2=16(y+1)