Find the locus of the moving point P such that 2PA =3PB , where A is(0,0) and B(4,-3).
Given, A is(0,0) and B(4,-3) and 2PA = 3PB
The equation of the locus of the moving point P is find out by considering the co-ordinates of P(x,y).
2 PA = 3 PB
Squaring both sides, we get
4 PA2 = 9 PB2
4[(x-0)2 + (y-0)2] = 9[(x - 4)2 + (y + 3)2]
⇒ 4x2 + 4y2 = 9[x2 + 16 - 8x + y2 + 9 + 6y]
⇒ 4x2 + 4y2 = 9x2 - 72x + 9y2 + 225 + 54y
⇒ 5x2 + 5y2 - 72x + 54y + 225 = 0