# How do I use completing the square to convert the general equation of a hyperbola to standard form?

##### 1 Answer

I can not remember how to deal with

Consider the equation below

The first thing that we should do is group our

Now, let's make our work easier by factoring out

Before proceeding, let's recall what happens when a binomial is squared

when a = 1, we have

Now, in our equation,

We want

In order to do that, we need to add a 3rd element.

We know that in

For

Meanwhile, for

For

We added something in the left-hand side of the equation.

Since we our dealing with an equality, we need to maintain the

equality.

We can do this by adding the same value in the right-hand side of the equation or by subtracting the same value in the left-hand side.

For this demonstration, I will subtract the same value in the left-hand side

Now that we have our perfect square trinomials and our equality remains to be one, we can proceed to simplifying the equation

Now we have transformed our general equation to standard form.

Take note that we can do the same trick to transform other conic sections into their standard form.