Which conic is x^2 - 4y^2 = 4

Step by step

The question

Question: name the conic and write in standard form x² − 4y² − 4 = 0.

1 Name the conic

Look at the squares.

x² and y² have different signs.

So it is a hyperbola.

2 Move the number

Move the plain number to the right: − 4 becomes + 4.

3 Make the right side 1

Divide every part by 4, so the right side is 1.

4/4 is 1/1.

That is the standard form of a hyperbola with center (0, 0).

4 Check

Let's check with a point on it: (2, 0), a vertex.

Put it in the first equation.

We get 0, like the first equation says.

So the standard form is right!

Let's look back.

First: name the conic.

Then: move the number.

Then: make the right side 1.

Last: check.