Question

If A(4,1)and B(5,4)find the equation on office the locus of point p if PA2=3PB2

Answer 1

Answer:

Let, the co-ordinate of P be (h,k)

PA = √{(h-4)²+(k-1)²}

PB =√{(h-5)²+(k-4)²}

Now,

PA2=3PB2

or, {(h-4)²+(k-1)²}=3 × {(h-5)²+(k-4)²}

or, (h²-8h+16+k²-2k+1)=3(h²-10h+25+k²-8k+16)

or, 2h²-22h+2k²-22k+106=0

or, h²-11h+k²-11k+53=0

so, the locus of P is,

x²-11x+y²-11y+53=0