algebra-conic sections parabola  TOPIC_SOLVED

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algebra-conic sections parabola

Postby sri340 on Wed Nov 16, 2011 1:13 pm

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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Re: algebra-conic sections parabola  TOPIC_SOLVED

Postby nona.m.nona on Wed Nov 16, 2011 8:02 pm

sri340 wrote: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 ?

The generic formula for this particular conic is 4p(x - h) = (y - k)2, where (h, k) is the vertex and 2p is the distance between the directrix and the focal point. (explanation)

Since the y-axis is the directrix, then the vertex and focal point are directly to the right, given the locations of the two listed points. By definition, then, the vertex must be at the point (h, k) = (p, k). Use this information, along with the two given points, to create a system of two equations in two unknowns.
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