Question

Find the points on y-axis which are at a distance of 13 units from B(5, 14).

Answer 1

Given:

Point B = (5, 14), and we need to find the points on the (y)-axis which are at a distance of 13 units from B.

A general point on the (y)-axis has coordinates (0, y) because on the (y)-axis, the (x)-coordinate is 0.

The distance between B(5, 14) and any point (0, y) on the (y)-axis is given by the distance formula:

`"Distance" = sqrt((x_2 − x_1)^2 + (y_2 − y_1)^2)`

This distance is given as 13 units:

\[ \sqrt{(0-5)^2 + (y - 14)^2} = 13 \]

Square both sides to remove the square root:

(0 − 5)² + (y − 14)² = 13² 

25 + (y − 14)² = 169

(y − 14)² = 169 − 25 = 144   ...[Simplify]

y − 14 = ±12

y = 14 + 12 = 26 or y = 14 − 12 = 2

The points on the (y)-axis that are at a distance of 13 units from B(5, 14) are (0, 26) and (0, 2).