Question

Find the points on the x-axis, each of which is at a distance of 10 units from the point A(11, –8).

Answer 1

Let P(x, 0) be the point on the x-axis.

Then as per the question we have

AP = 10

`\implies sqrt((x - 11)^2 + (0 + 8)^2` = 10

`\implies` (x – 11)² + 8² = 100          ...(Squaring both sides) 

`\implies` ( x – 11)² = 100 – 64

`\implies` ( x – 11)² = 36

`\implies` x – 11 = ±6

`\implies` x - 11 = 6 or x - 11 = -6

`\implies` x = 6 + 11 or x = -6 + 11

`\implies` x = 17 or x = 5

Hence, the points on the x-axis are (17, 0) and  (5, 0).