Answer:
To put the equation of an ellipse in standard form, we need to complete the square for both the x and y terms.
First, let's get all the x terms on the left and all the y terms on the right.
2x - 4x = -2x 3y² + 12y = 3y(y + 4)
Then, we can complete the square for the x terms by adding and subtracting 1/4 of the coefficient of the x term squared. For the y terms, we add and subtract 1/4 of the coefficient of the y term squared.
(-2x)² + (1/4)(-2)² = (-2x + 1)² - 1 = 1 (3y)² + (1/4)(3)² = (3y + 1.5)² - 1.5² = 9
So the standard form equation for the ellipse is:
(x + 1)²/1 + (y + 1.5)²/9 = 1
This can be rewritten as:
x²/1 + y²/9 = 1