Geo5.1.2

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Write the equation of the parabola whose focus is (-1,1) and directrix is 4x+3y+2=0\,

Given S=(-1,1)\, and l=4x+3y+2=0\,

Let P(x,y)\, be any point on the parabola.

SP^{{2}}=PM^{{2}}\,

(x+1)^{2}+(y-1)^{2}={\frac  {4x+3y+2}{{\sqrt  {16+9}}}}^{{2}}\,

25(x^{2}+y^{2}+1+2x-2y+1)=(16x^{2}+9y^{2}+4+24xy+12y+16x)\,

9x^{2}-24xy+16y^{2}+34x-62y+46=0\,

Main Page:Geometry:The Parabola