Question

Find a relation between x and y such that the point (x, y) is equidistant from the points (7, 1) and (3, 5).

Answer 1

Let P(x, y); A(7, 1); B(3, 5) 

The distance between points (x₁, y₁) and (x₂, y₂) is

by the sum, PA = PB

50 – 14x + x² – 2y + y² 

= 34 – 6x + x² – 10y + y² 

50 – 14x – 2y – 34 + 6x + 10y = 0 

-8x + 8y + 16 = 0 

-x + y + 2 = 0 , 

∴ x = y + 2