locus (1 Viewer)

[apak]

find the equation of the locus of a point P that moves so that PA is twice the distance of PB where A=(0,3) B= (4,7)

my answer is different from the answer book
dont you solve it as PA = 2PB

 

[Trev]

Yes, so:
√[x²+(y-3)²]=2√[(x-4)²+(y-7)²]
x²+(y-3)²=4[(x-4)²+(y-7)²]
etc.

 

[Wackedupwacko]

4PB²=PA²
4[ (x-4)² + (y-7)²] = x² + (y-3)²
4x²-32x+64+4y²-56y+196 = x² + y² - 6y + 9
3x²-32x+3y²-50y+251 =0 <---- if this isnt answer then continue
x²- 32x/3 + y² - 50y/3 = -251/3
complete the square
(x - 16/3)² + (y - 25/3)² = -251/3 + 256/9 + 625/9
(x - 16/3)² + (y - 25/3)² = 128/9