Question

Find the area of the region enclosed by the graph of $x^2 + y^2 = 2x - 6y + 6$.

Answer 1

Complete the squares to get

$x^2+y^2=2x-6y+6$

$\implies(x^2-2x+1)+(y^2+6y+9)=16$

$\implies(x-1)^2+(y+3)^2=4^2$

which is the equation of a circle centered at (1, -3) with radius 4, and thus with area 16π.