Q) Find the area contained within the graph of the equation:

A)

x^2 - 6x + y^2 + 12y = 0

Form perfect squares:

x^2 - 6x + 9 - 9 + y^2 + 12y + 36 - 36 = 0

(x + 3)^2 + (y + 6)^2 = 45

(x + 3)^2 + (y + 6)^2 = [sqrt(45)]^2

This is the equation of a circle, with radius sqrt(45)

so area = pi.r^2

= 45.pi

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