Multiple choice

Calculate the area enclosed by the circle represented by $\displaystyle (x+2)^2+(y+3)^2=25$

  1. $4\pi$
  2. $5\pi$
  3. $16\pi$
  4. $25\pi$
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D Correct answer
Explanation

The equation (x+2)^2 + (y+3)^2 = 25 represents a circle with radius squared = 25, so r = 5. Area = pi * r^2 = 25 * pi.

AI explanation

The equation of the circle is (x + 2)^2 + (y + 3)^2 = 25, which is in the standard form (x - h)^2 + (y - k)^2 = r^2. This reveals that the square of the radius is 25. The area of a circle is found using the formula Area = (pi)(r^2), so substituting r^2 = 25 gives an area of 25(pi).

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