Geo5.1.5

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Find the equation of the parabola whose axis is parallel to the Y-axis and which passes through the points (4,5),(-2,11),(-4,21)\,

The equation of the parabola with axis parallel to the y-axis is of the form

y=lx^{2}+mx+n\,

Since the parabola passes through the points (4,5),(-2,11),(-4,21)\,

5=16l+4m+n,11=4l-2m+n,21=16l-4m+n\,

Solving these three,we get

12l+6m=-6,12l-2m=10\,

8m=-16,m=-2,12l+4=10,l={\frac  {1}{2}},8-8+n=5,n=5\,

Hence the equation is

x^{2}-4x-2y+10=0\,


Main Page:Geometry:The Parabola