Question

2.
Let A=(1,0).B=(-1,0); C = (2,0 ) then the locus of P such that PB2 + PC?=2PA is
1) a straight line parallel to x-axis
3) pair of straight lines
2) a straight line parallel to y-axis
4) xy=0​

Answer 1

Step-by-step explanation:

Let P=(x,y)

Then, PA=

(x−1)

2

+y

2

...(i)

PB=

(x+1)

2

+y

2

...(ii)

PC=

(x−2)

2

+y

2

...(iii)

Hence, PC

2

+PB

2

=2PA

2

⇒[(x−2)

2

+y

2

]+[(x+1)

2

+y

2

]=2(x−1)

2

+2y

2

⇒(x−2)

2

+(x+1)

2

+2y

2

=2(x−1)

2

+2y

2

⇒(x−2)

2

+(x+1)

2

=2(x−1)

2

⇒(x

2

−4x+4)+(x

2

+2x+1)=2(x

2

−2x+1)

⇒2x

2

−2x+5=2x

2

−4x+2

⇒2x+3=0

⇒x=

2

−3

Hence, this represents a line parallel to y-axis.