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A and B are two given points whose coord...

A and B are two given points whose coordinates are (-5,3) and (2,4) respectively . A point P moves in such a manner that `PA:PB=3:2` . Find the equation to the locus traced out by P. What curve does it represent?

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The correct Answer is:
`5x^(2)+5y^(2)-76x-48y+44=0` …. (1)
We see that the equation (1) is a second degree equation in x,y and its coefficients of `x^(2)andy^(2)` are equal and coefficient of xy is zero . Therefore , equation (1) represents a circle. Therefore , the locus of P represents the equation of a circle .
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