Final answer:
The standard form of the equation of a circle is (x - h)² + (y - k)² = r². To convert the given equation, complete the square for x and y terms to get 3(x + 5)² + 3(y - 4)² = 381.
Step-by-step explanation:
The standard form of the equation of a circle is given by (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius.
To convert the given equation, we need to complete the square for both x and y terms. First, rearrange the equation to group the x terms and y terms together: 3x² + 30x + 3y² - 24y - 12 = 0.
Next, complete the square for x by adding (30/2)² = 225 to both sides, and complete the square for y by adding (-24/2)² = 144 to both sides. The equation becomes 3(x + 5)² + 3(y - 4)² = 381, which is now in the standard form of the equation of a circle.