Question

Find all points having an x coordinate of 5 whose distance from the point (2,2) is 5.

Answer 1

(5,6) , (5,-2)

Explanation:

Let the required point be P(5,y).

Its distance from (2,2) is 5 units.

So,
`(5-2)^(2)` +
`(y-2)^(2)` = 25.

So,
`3^(2)` +
`(y-2)^(2)` = 25.

9 +
`(y-2)^(2)` = 25.

`(y-2)^(2)` = 16

Two cases are possible for now

case 1 : y-2 = 4 .

y = 6

required point will be (5,6)

case 2 : y - 2 = -4.

y = -2.

required point will be (5,-2).

Two points are possible : (5,6) , (5,-2).