Multiple choice

The area of the circle whose centre is (1,2) and which passes through the point (4,6) is

  1. $ 25\pi $
  2. $ 100\pi$
  3. $92\pi $

  4. None of these
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A Correct answer
Explanation

The radius is the distance between (1,2) and (4,6): r = sqrt((4-1)^2 + (6-2)^2) = sqrt(3^2 + 4^2) = sqrt(9+16) = 5. Area = pi * r^2 = 25pi.

AI explanation

The radius of the circle is the distance between the center (1,2) and the point (4,6), calculated using the distance formula as the square root of ((4-1) squared + (6-2) squared). This gives the square root of (9 + 16), which is the square root of 25, so the radius is 5 units. The area of the circle is pi * r squared, giving pi * 5 squared = 25pi.

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