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Find the equation of the locus of a point p (x, y) such t...

Find the equation of the locus of a point p (x, y) such that pv = pw, where v= (1, 1) and w = (3, 5)

A.

2x + 2y = 9

B.

2x + 3y = 8

C.

2x + y = 9

D.

x + 2y = 8

Correct answer is D

The locus of a point p(x, y) such that pv = pw where v = (1, 1)

and w = (3, 5). This means that the point p moves so that its distance from v and w are equidistance

(xx1)2+(yy1)2 = (xx2)2+(yy2)2

(x1)2+(y1)2 = (x3)2+(y5)2

square both sides
(x - 1)2 + (y - 1)2 = (x - 3)2 + (y - 5)2

x2 - 2x + 1 + y2 - 2y + 1 = x2 - 6x + 9 + y2 - 10y + 25

x2 + y2 -2x -2y + 2 = x2 + y2 - 6x - 10y + 34

Collecting like terms
x2 - x2 + y2 - y2 - 2x + 6x -2y + 10y = 34 - 2

4x + 8y = 32

Divide through by 4

x + 2y = 8