Question

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

• A. \(2\sqrt{2}\)
• B. \(\sqrt{2}\)
• C. \(\sqrt{26}\)
• D. \(1\)

Hint:

Always double-check signs when subtracting negative coordinates in the distance formula. \(0 - (-1)\) becomes \(+1\).

Answer 1

The Correct Option is B

To find the radius of a circle centered at \((-1, 2)\) that passes through the point \((0, 3)\), we can use the distance formula. The radius \( r \) of the circle is the distance between the center \((-1, 2)\) and any point on the circle \((0, 3)\).

The distance formula is given as:

\(r = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)

• \(x_1 = -1\) and \(y_1 = 2\) are the coordinates of the center.
• \(x_2 = 0\) and \(y_2 = 3\) are the coordinates of the point the circle passes through.

Substitute these values into the distance formula:

\(r = \sqrt{(0 - (-1))^2 + (3 - 2)^2}\)

\(r = \sqrt{(0 + 1)^2 + (3 - 2)^2}\)

\(r = \sqrt{1^2 + 1^2}\)

\(r = \sqrt{1 + 1}\)

\(r = \sqrt{2}\)

Therefore, the radius of the circle is \(\sqrt{2}\).

Thus, the correct answer is \(\sqrt{2}\).