Which conic is y^2 - 12x = 0

Step by step, with the reason for every step · Conics from the general form · Precalculus

Step by step

Question: name the conic and write in standard form y² − 12x = 0.

y² − 12x = 0

Look at the squares.

Only y² is here.

So it is a parabola.

only x² or only y² → parabola ✓

x² and y², same number in front → circle

same signs, different numbers → ellipse

different signs → hyperbola

Keep the y terms on the left.

Move − 12x and the plain number to the right: their signs change.

(y²) = 12x

That is the standard form of a parabola: y² = 12x.

Let's check with a point on it, (3, 6).

Put it in the first equation.

6² − 12 × 3 = 36 − 36 = 0

We get 0, like the first equation says.

So the standard form is right!

Let's look back.

First: name the conic.

Then: keep y on the left.

Last: check.

Answer

(y²) = 12x

Try this one yourself, then check:

Name the conic and write in standard form y² − 8x = 0

Show the answer

y² = 8x