Hyperbolas Page 8

Page 8

Rewriting the Equation of a Hyperbola
from General to Standard Form

Like the general equation of a circle and an ellipse, the general equation of a hyperbola does not easily tell you what a certain hyperbola looks like.

Therefore, when given an equation of a hyperbola in general form, you want to rewrite it into the standard form which provides more information about the graph.

Similar to the circle and the ellipse, you can use a method called completing the square to rewrite general equations of hyperbolas into standard form.

Let's look at a few examples.

Summary of Steps

STEP 1: Collect like terms together.
STEP 2: Move constant terms to the right hand side of the equal sign.
STEP 3: Factor out the coefficient of x² from each x term.
Factor out the coefficient of y² from each y term.
STEP 4: Complete the squares if necessary. Add numbers to both sides of the equation.
STEP 5: Simplify.
STEP 6: Divide the entire equation by an appropriate number so that the right hand side becomes 1.
STEP 7: Simplify any fractions.
In the following questions, you will practise converting the equations of hyperbolas from general form to standard form.

STEP 1:	Collect like terms together.
STEP 2:	Move constant terms to the right hand side of the equal sign.
STEP 3:	Factor out the coefficient of x² from each x term. Factor out the coefficient of y² from each y term.
STEP 4:	Complete the squares if necessary. Add numbers to both sides of the equation.
STEP 5:	Simplify.
STEP 6:	Divide the entire equation by an appropriate number so that the right hand side becomes 1.
STEP 7:	Simplify any fractions.
In the following questions, you will practise converting the equations of hyperbolas from general form to standard form.