Find the co-ordinates of the points on the y-axis, which are at a distance of 10 units from the point (-8, 4).

Let (0, y) = (x₁, y₁) and (-8, 4) = (x₂, y₂)

⇒ Distance between the given points =

$\sqrt{(x$2 - x1)^2 + (y2 - y1)^2}\\[1em] ⇒ 10 = \sqrt{(-8 - 0)^2 + (4 - y)^2}\\[1em] ⇒ 10 = \sqrt{(-8)^2 + (4 - y)^2}\\[1em] ⇒ 10^2 = 64 + 16 + y^2 - 8y\\[1em] ⇒ 100 = 80 + y^2 - 8y\\[1em] ⇒ 80 + y^2 - 8y - 100 = 0 \\[1em] ⇒ y^2 - 8y - 20 = 0 \\[1em] ⇒ y^2 - (10y - 2y) - 20 = 0 \\[1em] ⇒ y^2 - 10y + 2y - 20 = 0 \\[1em] ⇒ (y^2 - 10y) + (2y - 20) = 0 \\[1em] ⇒ y(y - 10) + 2(y - 10) = 0 \\[1em] ⇒ (y - 10)(y + 2) = 0 \\[1em] ⇒ y = 10 \text{ and } -2

Hence, the co-ordinates of points are (0, 10) and (0, -2).