Alg6.25

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Find the locus of P,if the ratio of the distances from P to (5,-4),(7,6)\, is 2:3.

Let P be (x,y) and the given points be A,B.The given geometric condition is

{\frac  {PA}{PB}}={\frac  {2}{3}}\,

3PA=2PB\,

Squaring on both sides,

9PA^{{2}}=4PB^{{2}}\,

(x-5)^{2}+(y+4)^{2}=(x-7)^{2}+(y-6)^{2}\,

x^{2}+25-10x+y^{2}+16+8y=x^{2}+49-14x+y^{2}+36-12y\,

14x-10x+8y+12y=85-25-16\,

4x+20y=44\,

x+5y=11\,

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