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:

When subtracting negative coordinates in the distance formula, pay extra attention to sign changes.
Writing \(x_2 - x_1\) as \(0 - (-1) = 1\) is correct, whereas a common sign error is writing it as \(0 - 1 = -1\).
Although squaring eliminates sign errors, practicing meticulous steps avoids other common pitfalls!

Answer 1

The Correct Option is B

Step 1: Understanding the Question:
The topic of this question is Coordinate Geometry.
We are given a circle with a center located at the point \(C(-1, 2)\).
We are also told that the circle passes through the point \(P(0, 3)\).
The radius of the circle is defined as the distance between the center of the circle and any point lying on its circumference.
Therefore, the radius of the circle is equal to the distance between points \(C\) and \(P\).

Step 2: Key Formula or Approach:
We will use the standard distance formula to calculate the distance between the center \(C(x_1, y_1) = (-1, 2)\) and the point \(P(x_2, y_2) = (0, 3)\):
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Step 3: Detailed Explanation:

• Identify the coordinates of the two key points:
Center of the circle, \((x_1, y_1) = (-1, 2)\)
Point on the circumference, \((x_2, y_2) = (0, 3)\)

• Substitute these coordinates into the distance formula to compute the radius \(r\):
\[ r = \sqrt{(0 - (-1))^2 + (3 - 2)^2} \]

• Simplify the terms inside the square root:
\[ r = \sqrt{(0 + 1)^2 + (1)^2} \] \[ r = \sqrt{1^2 + 1^2} \] \[ r = \sqrt{1 + 1} = \sqrt{2} \text{ units} \]

Step 4: Final Answer:
The radius of the circle is \(\sqrt{2}\).
Therefore, the correct option is (B).