Geo5.1.7

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Find the equation of the parabola whose axis is parallel to X-axis and passing through the points (-1,3),(-2,1),(1,2)\,

The equation of the parabola whose axis is parallel to x-axis is x=ly^{2}+my+n\,

The parabola passes through (-1,3),(-2,1),(1,2)\,

-1=9l+3m+n,-2=l+m+n,1=4l+2m+n\,

8l+2m=1,3l+m=3\,

2l=-5,l={\frac  {-5}{2}},m={\frac  {21}{2}}\,

n+8=-2,n=-10\,

Therefore,the equation of the parabola is

2x=-5y^{2}+21y-10\,

5y^{2}-21y+2x+20=0\,


Main Page:Geometry:The Parabola