Which conic is 4x^2 + 9y^2 = 36

Step by step

The question

Question: name the conic and write in standard form 4x² + 9y² − 36 = 0.

1 Name the conic

Look at the squares.

x² and y² have the same sign, but 4 and 9 are different numbers.

So it is an ellipse.

2 Move the number

Move the plain number to the right: − 36 becomes + 36.

3 Make the right side 1

Divide every part by 36, so the right side is 1.

4/36 is 1/9.

9/36 is 1/4.

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

4 Check

Let's check with a point on it: (3, 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.