Multiple choice

The area of the circle centred at $\left( 1,2 \right)$ and passing through $ \left( 4,6 \right) $ is

  1. $5 \pi$
  2. $10 \pi$
  3. $25 \pi$

  4. None of these
Reveal answer Fill a bubble to check yourself
C Correct answer
Explanation

Radius squared = (4-1)^2 + (6-2)^2 = 3^2 + 4^2 = 9 + 16 = 25. Area = pi * r^2 = 25 * pi.

AI explanation

The radius of the circle is the distance between the points (1, 2) and (4, 6). Using the distance formula, we calculate the radius squared as (4 - 1)^2 + (6 - 2)^2, which equals 3^2 + 4^2, resulting in 25. The area of the circle is pi multiplied by the radius squared, giving 25 pi.

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