Question

PA + PB = 2PC. Find the locus of P.
'[March 19TS, 17AP, May 1513
ii) Find the locus of the point P such that PA’ + PB= 2c where A(a,0), B(-a, 0)
and 0 < | a l < | c l .​

Answer 1

Answer:

Given,

PA=PB.

or,

x

2

+(y−3)

2

+(z−2)

2

=

(x−2)

2

+(y−4)

2

+(z−1)

2

or, −6y+9−4z+4=−4x+4−8y+16−2z+1 [ Squaring and then eliminating the higher power of x,y,z]

or,4x+2y−2z=8

or, 2x+y−z=4.

So locus of P is 2x+y−z=4.