Multiple choice

Determine the area enclosed by the curve $\displaystyle x^{2}-10x+4y+y^{2}=196$

  1. $15\pi$
  2. $225\pi$
  3. $20\pi$
  4. $17\pi$
Reveal answer Fill a bubble to check yourself
B Correct answer
Explanation

Rearranging the equation: (x^2 - 10x + 25) + (y^2 + 4y + 4) = 196 + 25 + 4. This simplifies to (x-5)^2 + (y+2)^2 = 225. This is a circle with radius squared = 225, so radius = 15. Area = pi * r^2 = 225 * pi.

AI explanation

Rewrite the curve equation by completing the square for the x and y terms to get (x minus 5) squared plus (y plus 2) squared equals 225. This represents a circle with a radius squared of 225. Using the area of a circle formula, pi times the radius squared, the enclosed area is 225 pi.

Keep practicing — related questions