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.
