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