# How do you convert this equation #4x ^ { 2} + 8x + 3y ^ { 2} - 12y + 1= 0# to its graphable form?

##### 2 Answers

#### Explanation:

This equation can be made into its graphable form by completing the square.

Let's complete the square for

Now for

And there's your graphable form.

Hope this helps!

Please see below.

#### Explanation:

or

or

or

or

Hence, it is an equation of an ellipse, whose major axis is vertical (parallel to

Its center is

graph{(4x^2+8x+3y^2-12y+1)((x+1)^2+(y-2)^2-0.01)((x+1)^2+(y-2+sqrt(5/4))^2-0.01)((x+1)^2+(y-2-sqrt(5/4))^2-0.01)=0 [-7, 6, -1, 5]}