Geo5.1.6

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Find the equation of the parabola whose axis is parallel to X-axis and which passes through (3,3),(6,5),(6,-3)\,

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

The parabola passes through (3,3),(6,5),(6,-3)\,

3=9l+3m+n,6=25l+5m+n,6=9l-3m+n\,

-3=6m,m={\frac  {-1}{2}}\,

9l+n={\frac  {9}{2}},25l+n={\frac  {17}{2}}\,

-16l=-4,l={\frac  {1}{4}}\,

{\frac  {9}{4}}-{\frac  {3}{2}}+n=3,4n=0,n=0\,

Hence the required parabola is

4x=y^{2}-2y\,

(y-2)^{2}=4(x+1)\,


Main Page:Geometry:The Parabola