Find the area of the region enclosed by the graph of x^2+y^2=2x-6y+16+4x+12y+40

cooIcooIcooI17 Jul 21, 2024

#1**+1 **

First, moving all terms to one side other than the constants, we get

\(x^2+y^2-6x-6y=56\)

Completing the square for both x and y, we get

\(\left(x-3\right)^2+\left(y-3\right)^2=\left(\sqrt{74}\right)^2\)

Thus, the radius is

\(r=\sqrt{74}\)

Using the circle equation, we have

AREA OF CIRCLE = \(\sqrt{75}^2\pi = 74\pi\)

Thus, 74pi is the answer.

Thanks! :)

NotThatSmart Jul 21, 2024