Question

What is the area of the region bounded by the graph of the equation x^2+y^2 + 3 = -4y + 6x-1?

Answer 1

What’s a region bounded by mean?

Answer 2

9π

Explanation:

What we need to do here is convert this equation into a standard circle equation;

x^2+y^2 + 3 = -4y + 6x-1,

x^2+y^2+4y-6x+1 = 0,

x^2-6x+(-3)^2 + y^2+4y+(2)^2 = 3^2

(x-3)^2 + (y+2)^2 = 3^2,

so we have a circle with a radius of 3, and hence the area of our region is π(3)^2 = 9π. correct!