Algebra Examples

Find the Center and Radius
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 an ellipse. Use this form to determine the values used to find the center along with the major and minor axis of the ellipse.
Match the values in this ellipse to those of the standard form. The variable represents the radius of the major axis of the ellipse, represents the radius of the minor axis of the ellipse, represents the x-offset from the origin, and represents the y-offset from the origin.
The center of an ellipse follows the form of . Substitute in the values of and .
Find , the distance from the center to a focus.
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Find the distance from the center to a focus of the ellipse by using the following formula.
Substitute the values of and in the formula.
Simplify.
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Remove parentheses around .
One to any power is one.
Apply the product rule to .
One to any power is one.
Raise to the power of to get .
To write as a fraction with a common denominator, multiply by .
Write each expression with a common denominator of , by multiplying each by an appropriate factor of .
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Combine.
Multiply by to get .
Combine the numerators over the common denominator.
Multiply by to get .
Multiply by to get .
Subtract from to get .
Rewrite using the quotient rule for radicals.
Simplify the denominator.
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Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Find the vertices.
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The first vertex of an ellipse can be found by adding to .
Substitute the known values of , , and into the formula.
Simplify.
The second vertex of an ellipse can be found by subtracting from .
Substitute the known values of , , and into the formula.
Simplify.
Ellipses have two vertices.
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Find the foci.
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The first focus of an ellipse can be found by adding to .
Substitute the known values of , , and into the formula.
Simplify.
The second vertex of an ellipse can be found by subtracting from .
Substitute the known values of , , and into the formula.
Simplify.
Ellipses have two foci.
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:
These values represent the important values for graphing and analyzing an ellipse.
Center:
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:
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:
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