Question

If A =(-2,3) and B=(4,1) are given points find the equation of locus of point P, such that PA=2PB.

Answer 1

$\text{Let the moving point be P(h,k)}$

$\text{Given points are A(-2,3) and B(4,1)}$

$\text{Given condition is PA=2 PB}$

$\sqrt{(h+2)^2+(k-3)^2}=2\;\sqrt{(h-4)^2+(k-1)^2}$

$\text{Squaring on both sides, we get}$

$(h+2)^2+(k-3)^2=4[(h-4)^2+(k-1)^2]$

$h^2+4+4h+k^2+9-6k=4[h^2+16-8h+k^2+1-2k]$

$h^2+4+4h+k^2+9-6k=4h^2+64-32h+4k^2+4-8k]$

$3h^2+3k^2-36h-2k+55=0$

$\therefore\textbf{The locus of P is}$

$\bf\,3x^2+3y^2-36x-2y+55=0$

Find more:

B and c are fixed points having coordinates (3,0) and (-3,0) respectively. If the vertical angle bac is 90 then locus

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