Alg6.23

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A(2,3),B(-3,4)\, be given two points.Find the locus of P so that the area of the triangle PAB is 8.5square units.

Let P(x,y) be a point in locus.

The area of the triangle is

{\frac  {1}{2}}|[2(4-y)-3(y-3)+x(3-4)]|={\frac  {17}{2}}\,

|8-2y-3y+9-x|=17\,

|17-x-5y|=17\,

x+5y=0,x+5y=34\,

Equation of the locus of P is

(x+5y)(x+5y-34)=0\,

x^{2}+10xy+25y^{2}-34x-170y=0\,


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