Question

Find the equation of the locus of P , if A = (4,0),B=(-4,0) and PA-PB =4

Answer 1

A=4,0

B=-4,0

mod PA-PB=4

PA-PB=+_4

PA=+_4+PB

PA^2=16+PB^2+_8PB

PA^2-16+PB^2=+_8PB

(x-4)^2+y^2-(x+4)^2-y^2-16=+_8

x^2+16-8x-(x^2+16+8x)-16=+_8

16-16-8x-8x-16=+_8

-16x-16=+_8

16(-x-1)=+_8

-x-1=+_1/2

squaring on both sides

-(x-1))^2=+1/2PB^2

-(x^2-2x+1)=1/2(x+4)^2+y^2

-x^2+2x-1=1/4(x^2+8x+16+y^2)

-3x^2/2-y^2/2=3 is the locus of P

@skb

Answer 2

Answer:

please ignore the minor mistakes made

hope it helps!!!!!!