Question

The number of points on x-axis which are at a distance of `2sqrt(5)` from the point (7, 4), is ______.

Answer 1

The number of points on x-axis which are at a distance of `2sqrt(5)` from the point (7, 4), is 2.

Explanation:

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

Distance PQ from P to Q(7, 4) is `sqrt((x - 7)^2 + (0 - 4)^2] = 2sqrt(5)`. 

Squaring: (x – 7)² + 16 = 20 

⇒ (x – 7)² = 4 

⇒ x – 7 = ±2

⇒ x = 9 or x = 5

So the two points are (9, 0) and (5, 0), i.e. two such points.