Trigonometry Examples

Find the Vertices (y^2)/6-(x^2)/12=1
Step 1
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 .
Step 2
This is the form of a hyperbola. Use this form to determine the values used to find vertices and asymptotes of the hyperbola.
Step 3
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, .
Step 4
Find the vertices.
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Step 4.1
The first vertex of a hyperbola can be found by adding to .
Step 4.2
Substitute the known values of , , and into the formula and simplify.
Step 4.3
The second vertex of a hyperbola can be found by subtracting from .
Step 4.4
Substitute the known values of , , and into the formula and simplify.
Step 4.5
The vertices of a hyperbola follow the form of . Hyperbolas have two vertices.
Step 5