Which conic is 9x^2 + y^2 - 9 = 0

Step by step

The question

Question: name the conic and write in standard form 9x² + y² − 9 = 0.

1 Name the conic

Look at the squares.

x² and y² have the same sign, but 9 and 1 are different numbers.

So it is an ellipse.

2 Move the number

Move the plain number to the right: − 9 becomes + 9.

3 Make the right side 1

Divide every part by 9, so the right side is 1.

9/9 is 1/1.

That is the standard form of an ellipse with center (0, 0).

4 Check

Let's check with a point on it: (1, 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.