The equation 36x² + 4y² - 288x + 16y + 448 = 0 to standard form is (x - 4)² + (y + 2)²/9 = -20
Converting the equation to standard form
From the question, we have the following parameters that can be used in our computation:
36x² + 4y² - 288x + 16y + 448 = 0
Rewrite as
36x² + 4y² - 288x + 16y + 448 = 0
Group the equation by the variables
36x² - 288x + 4y² + 16y = -448
So, we have
36(x² - 8x) + 4(y² + 4y) = -448
Complete the square on x and y
So, we have
36(x - 4)² + 4(y + 2)² = -448 + 16 - 288
This gives
36(x - 4)² + 4(y + 2)² = -720
Next, we divide through by 36
(x - 4)² + (y + 2)²/9 = -20
Hence, the equation is (x - 4)² + (y + 2)²/9 = -20