Find the equation of the locus of a point p (x, y) such that pv…

Correct Answer: Option D

Explanation

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
(sqrt{(x − x_1)^2 + (y − y_1)^2}) = (sqrt{(x − x_2)^2 + (y − y_2)^2})
(sqrt{(x -1)^2 + (y – 1)^2}) = (sqrt{(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

There is an explanation video available below.