The equation for Circle M is shown below. What is the area of Circle M in terms of π? 4x2+4y2−40x+24y−5=0
Question 1 options:
141√2π square units
131√2πsquare units
1072.6π square units
1414πsquare units
1314π square units

 (141/4)pi

This looks like it matches up with choice D

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

step-by-step explanation:

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