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Transformations of a Hyperbola - Problem 5

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If an equation is given in general form, you'll know it represents a hyperbola if both the x and y terms are squared and are being subtracted. To get from general to standard form, re-arrange the equation so the x terms are together and the y terms are together, and then complete the square on each one. You should be adding two terms to both sides of the equation to keep the equation balanced. From there, you'll need to make the equation equal to one, so you'll need to divide all terms by whatever you have on the right side of the equation. Once the equation is in standard form, you can identify which direction is the axis of symmetry and find "a" and "b" to graph your asymptotes and hyperbola.

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