Question

Find a relation between x and y such that the point (x, y) is equidistant from the points (3, 6) and (- 3, 4).

Answer 1

Coordinates of the points are A(3, 6) and B(-3, 4) 

Let the point P(x, y) is equidistant from A and B 

Using distance formula = \(\sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

⇒ PA = PB

\(\sqrt{(x - 3)^2 + (y - 6)^2}\) = \(\sqrt{(x + 3)^2 + (y - 4)^2}\)

On squaring both sides, we get

(x - 3)² + (y - 6)² = (x + 3)² + (y - 4)²

x² - 6x + 9 + y² - 12y + 36 = x² + 6x + 9 + y² - 8y + 16

3x + y = 5