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

`⇒ sqrt((x-11)^2 +(0+8)^2)=10`

`⇒(x-11)^2 +8^2 = 100`            (Squaring both sides) 

`⇒ ( x -11)^2 =100-64=36`

`⇒ x -11= +-6`

`⇒ x = 11+-6`

⇒ x = 11  -6 , 11 + 6

⇒ x = 5, 17

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