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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. |
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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 | STEP 7: | Simplify any fractions.
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In the following questions, you will practise converting the equations of hyperbolas from general form to standard form.
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