Question

Find the point on the y-axis which is equidistant from the points (5, −2) and (−3, 2).

Answer 1

Since the point is on the y-axis so, X-coordinate is zero.
Let the point be (0, y)
Its distance from (5, –2) and (–3, 2) are equal

∴ `sqrt((0 -5)^2 + (y+2)^2) = sqrt((0+3)^2 + (y -2)^2)`

⇒ `25 + y^2  + 4y + 4 = 9 + y^2 - 4y + 4  ....["squaring both sides"]`

⇒ `4y + 29 = -4y + 13`

⇒ `4y + 4y = 13 - 29`

⇒`8y = (-16)/(8) = -2`

Thus, the point is (0,-2)