A certain parabola passes through the points (5,1) and (13,-7) and has the y-axis as its directrix.what are the coordinates of all points at which the vertex of this parabola could be located ?

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- Nov 18th 2011, 02:00 PMsri340algebra conic sections parabola
A certain parabola passes through the points (5,1) and (13,-7) and has the y-axis as its directrix.what are the coordinates of all points at which the vertex of this parabola could be located ?

- Nov 18th 2011, 04:15 PMTKHunnyRe: algebra conic sections parabola
y-axis as directrix, it looks like this: x = ay^2 + by + c and a > 0

Passing through (5,1), we have 5 = a + b + c

Passing through (13,-7), we have 13 = 49a - 7b + c

x-coordinate of Vertex must be on (0,5].

This all leads to a = (1/7)*(6-c), so 6-c > 0 or c < 6

Finally, b = (1/7)*(29-6c) and this suggests c > 2.27, approximately. I'll let you pin it down exactly.

Where does that leave us?