Question

Find d point which is equidistance from d point A (-5,4) & B (-1,6)? How many such points r there?

Answer 1

Let P(x, y) be the point which is equidistance from the points A(–5, 4) and B(–1, 6).

Then PA = PB

⇒ PA² = PB²

⇒ (x – (–5))² + (y – 4)² = (x – (–1))² + (y – 6)²

⇒ x² + 25 + 10x + y² + 16 – 8y = x² + 1 + 2x + y² + 36 – 12y

⇒10x – 2x – 8y + 12y + 41 – 37 = 0

⇒8x + 4y + 4 = 0

⇒2x + y + 1 = 0 .......... (1)

Hence all the point satisfying (1) i.e. lying on line (1) are equidistance from A and B.

There are infinite number of such points.