Question

IfA=(6,0) and B (0,4) and 0 is the origin,
then the locus of P such that area of POB
= 2(area of POA)​

Answer 1

Step-by-step explanation:

Let locus of point be P(x,y)

Given A(6,0) and B(0,4)

POB = 2POA

√((x - 0)^2 + (y - 4)^2) = 2 √((x - 6)^2 + (y - 0)^2)

Squaring on both sides

(x)^2 + (y - 4)^2 = 4( (x - 6)^2 + (y)^2)

x^2 + y^2 + 16 - 8y = 4 ( x^2 + 36 - 12x + y^2)

x^2 + y^2 + 16 - 8y = 4x^2 + 144 - 48x + 4y^2

4x^2 + 4y^2 - 48x + 144 - x^2 -y^2 + 8y - 16 = 0

3x^2 + 3y^2 - 48x + 8y - 128 = 0