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

Step 1: Understanding the Concept:
The radius of a circle is the distance between its center and any point on its circumference.
Step 2: Key Formula or Approach:
Distance formula: \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\)
Center \((x_1, y_1) = (-1, 2)\)
Point on circle \((x_2, y_2) = (0, 3)\)
Step 3: Detailed Explanation:
\[ \text{Radius } (r) = \sqrt{(0 - (-1))^2 + (3 - 2)^2} \]
\[ r = \sqrt{(1)^2 + (1)^2} \]
\[ r = \sqrt{1 + 1} = \sqrt{2} \]
Step 4: Final Answer:
The radius of the circle is \(\sqrt{2}\).