Precalculus Examples

Find the Circle Using the Diameter End Points
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The diameter of a circle is any straight line segment that passes through the center of the circle and whose endpoints are on the circumference of the circle. The given end points of the diameter are and . The center point of the circle is the center of the diameter, which is the midpoint between and . In this case the mid point is .
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Use the midpoint formula to find the midpoint of the line segment.
Substitute in the values for and .
Add and to get .
Divide by to get .
Add and to get .
Find the radius for the circle. The radius is any line segment from the center of the circle to any point on its circumference. In this case, is the distance between and .
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Use the distance formula to determine the distance between the two points.
Substitute the actual values of the points into the distance formula.
Simplify.
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Subtract from to get .
Raise to the power of to get .
Multiply by 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.
Simplify the numerator.
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Multiply by to get .
Multiply by to get .
Subtract from .
Move the negative in front of the fraction.
Apply the product rule to .
Raise to the power of to get .
Multiply by to get .
Apply the product rule to .
Raise to the power of to get .
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.
Simplify the numerator.
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Multiply by to get .
Add and .
Rewrite as .
Simplify the denominator.
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Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
is the equation form for a circle with radius and as the center point. In this case, and the center point is . The equation for the circle is .
The circle equation is .
Simplify the circle equation to get .
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