To convert the given equation into standard form, we need to rearrange it in the form of (x - h)² + (y - k)² = r², where (h, k) represents the center of the circle and r represents the radius.
The given equation is: 4x² + 9y² + 24x - 36y + 36 = 0.
Let's complete the square for the x terms first:
4x² + 24x --> 4(x² + 6x).
To complete the square, we need to add and subtract the square of half the coefficient of x:
4(x² + 6x + 9) - 4(9) --> 4(x + 3)² - 36.
Now, let's complete the square for the y terms:
9y² - 36y --> 9(y² - 4y).
Adding and subtracting the square of half the coefficient of y:
9(y² - 4y + 4) - 9(4) --> 9(y - 2)² - 36.
Combining the x and y terms:
4(x + 3)² - 36 + 9(y - 2)² - 36 + 36 = 0.
Simplifying the equation:
4(x + 3)² + 9(y - 2)² = 36.
Dividing both sides of the equation by 36:
(x + 3)²/9 + (y - 2)²/4 = 1.
Therefore, the standard form of the equation is:
(x + 3)²/9 + (y - 2)²/4 = 1.
Hence, the correct answer is: ○ (x+3)²/9 + (y-2)²/4 = 1.