How to write this conic section in standard form?

3y^2 = 108 - 12x^2

12x^2 + 3y^2 = 108

x^2/9 + y^2/36 = 1

To write the given equation of the conic section in standard form, you can follow these steps:

Step 1: Rearrange the equation to isolate the terms involving x and y on one side of the equation.
3y^2 = 108 - 12x^2

Step 2: Divide both sides of the equation by the constant term (108) to create a coefficient of 1 for the x^2 and y^2 terms.
(3y^2)/108 = (108 - 12x^2)/108

Simplifying further, we have:
y^2/36 = (108 - 12x^2)/108

Step 3: Move the constant term from the right side of the equation to the left side by subtracting (108/108 = 1) from both sides.
y^2/36 - 1 = (108 - 12x^2)/108 - 1

Simplifying and finding a common denominator, we get:
y^2/36 - 36/36 = (108 - 12x^2 - 108)/108

This simplifies to:
y^2/36 - 1 = -12x^2/108

Step 4: Simplify the equation further by dividing every term by the coefficient of the x^2 term (-12/108 = -1/9).
(y^2/36 - 1) = (-12x^2/108) / (-1/9)

Simplifying, we get:
(y^2/36 - 1) = (x^2/9)

Step 5: Finally, write the equation in standard form by reversing the order of the terms on the right side.
(y^2/36) = (x^2/9)

In standard form, the equation of the conic section is:
(x^2/9) = (y^2/36)