Geo5.1.9

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Find the equation of the parabola whose focus is (3,-4) and directrix is x+y+7=0\,

Let S=(3,-4)\, and l=x+y+7=0\,

P(x,y) be any point on the parabols.

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

(x-3)^{2}+(y+4)^{2}=({\frac  {x+y+7}{{\sqrt  {2}}}})^{{2}}\,

2(x^{2}+y^{2}-6x+8y+25)=x^{2}+y^{2}+2xy+14y+14x+49)\,

x^{2}+y^{2}-2xy-26x+2y+1=0\,


Main Page:Geometry:The Parabola