Trigonometry Examples

Find the Vertices 36y^2-9x^2=324
Find the standard form of the hyperbola.
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Divide each term by to make the right side equal to one.
Simplify each term in the equation in order to set the right side equal to . The standard form of an ellipse or hyperbola requires the right side of the equation be .
This is the form of a hyperbola. Use this form to determine the values used to find vertices and asymptotes of the hyperbola.
Match the values in this hyperbola to those of the standard form. The variable represents the x-offset from the origin, represents the y-offset from origin, .
Find the vertices.
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The first vertex of a hyperbola can be found by adding to .
Substitute the known values of , , and into the formula and simplify.
The second vertex of a hyperbola can be found by subtracting from .
Substitute the known values of , , and into the formula and simplify.
The vertices of a hyperbola follow the form of . Hyperbolas have two vertices.
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