Trigonometry Examples

Find the Foci (y^2)/144-(x^2)/25=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 distance from the center to a focus.
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Step 4.1
Find the distance from the center to a focus of the hyperbola by using the following formula.
Step 4.2
Substitute the values of and in the formula.
Step 4.3
Simplify.
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Step 4.3.1
Raise to the power of .
Step 4.3.2
Raise to the power of .
Step 4.3.3
Add and .
Step 4.3.4
Rewrite as .
Step 4.3.5
Pull terms out from under the radical, assuming positive real numbers.
Step 5
Find the foci.
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Step 5.1
The first focus of a hyperbola can be found by adding to .
Step 5.2
Substitute the known values of , , and into the formula and simplify.
Step 5.3
The second focus of a hyperbola can be found by subtracting from .
Step 5.4
Substitute the known values of , , and into the formula and simplify.
Step 5.5
The foci of a hyperbola follow the form of . Hyperbolas have two foci.
Step 6