Answer: (141/4)pi
This looks like it matches up with choice D
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Work Shown:
Let's complete the square for the x and y terms like so
4x^2 + 4y^2 - 40x + 24y - 5 = 0
4x^2 - 40x + 4y^2 + 24y = 5
4(x^2 - 10x + y^2 + 6y) = 5
x^2 - 10x + y^2 + 6y = 5/4
x^2 - 10x + 25 + y^2 + 6y = 5/4 + 25
(x^2 - 10x + 25) + y^2 + 6y = 5/4 + 100/4
(x-5)^2 + y^2 + 6y = 105/4
(x-5)^2 + y^2 + 6y + 9 = 105/4 + 9
(x-5)^2 + (y^2 + 6y + 9) = 105/4 + 36/4
(x-5)^2 + (y + 3)^2 = 141/4
The last equation is in the form (x-h)^2 + (y-k)^2 = r^2 where (h,k) = (5,-3) is the center and r^2 = 141/4 leads to r = sqrt(141)/2 which is the radius.
The area of the circle is therefore,
A = pi*r^2
A = pi*141/4
A = (141/4)pi
