Question

A circle centred at (–1, 2) passes through the point (0, 3). Radius of the circle is ______.

Options

• `2sqrt(2)`

• `sqrt(2)`

• `sqrt(26)`

• 1

Answer 1

A circle centred at (–1, 2) passes through the point (0, 3). Radius of the circle is `underlinebb(sqrt(2))`.

Explanation:

The radius of a circle is the distance between its center and any point on its circumference.

Distance formula: `d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

Center (x₁, y₁) = (–1, 2)

Point on circle (x₂, y₂) = (0, 3)

Radius (r) = `sqrt((0 - (-1))^2 + (3 - 2)^2`

`r = sqrt((1)^2 + (1)^2`

`r = sqrt(1 + 1)`

`r = sqrt(2)`

The radius of the circle is `sqrt(2)`.