Question

Find the radius of the circle whose centre is at (4, 5) and which passes through the point (1, 9).

1. 4 unit
2. 5 unit
3. 9 unit
4. 8 unit

Answer 1

Correct Answer - Option 2 : 5 unit

Concept:

Distance between two-point (x₁, y₁) and (x₂, y₂) is,

D = \(\rm \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}\)

Calculation:

Given:

Coordinate of the centre of the circle is (4, 5)

The circle passes through the point (1, 9)

The centre of the circle is at (4, 5). Since, the point (1, 9) lies on the circle, the distance of the

centre from this point is the radius r of the circle.

Radius, r = \(\rm \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2}\)

⇒ r = \(\sqrt{(1 – 4)^2 + (9 – 5)^2}\)

= \(\sqrt{9+16}\)

= 5

∴ The radius of a circle is 5 unit.