Alg6.21

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Find the equation of the locus of points which are equidistant from A(-3,2),B(0,4)\,

Let P(x,y) be a point in the locus.Then,the geometric condition is

AP=BP\,

AP^{{2}}=BP^{{2}}\,

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

x^{2}+9+6x+y^{2}+4-4y=x^{2}+y^{2}-8y+16\,

6x-4y+13+8y-16=0\,

6x+4y=3\,

Hence the equation of the locus is 6x+4y=3\,</math>


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