JAMB Mathematics 2017 Paper

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

√(x−x1)2+(y−y1)2 = √(x−x2)2+(y−y2)2

√(x−1)2+(y−1)2 = √(x−3)2+(y−5)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