Precalculus Examples

Find the Circle Using the Diameter End Points
Step 1
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 midpoint is .
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Step 1.1
Use the midpoint formula to find the midpoint of the line segment.
Step 1.2
Substitute in the values for and .
Step 1.3
Add and .
Step 1.4
Divide by .
Step 1.5
Add and .
Step 2
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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Step 2.1
Use the distance formula to determine the distance between the two points.
Step 2.2
Substitute the actual values of the points into the distance formula.
Step 2.3
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Step 2.3.1
Subtract from .
Step 2.3.2
Raising to any positive power yields .
Step 2.3.3
Write as a fraction with a common denominator.
Step 2.3.4
Combine the numerators over the common denominator.
Step 2.3.5
Subtract from .
Step 2.3.6
Move the negative in front of the fraction.
Step 2.3.7
Use the power rule to distribute the exponent.
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Apply the product rule to .
Apply the product rule to .
Step 2.3.8
Raise to the power of .
Step 2.3.9
Multiply by .
Step 2.3.10
One to any power is one.
Step 2.3.11
Raise to the power of .
Step 2.3.12
Add and .
Step 2.3.13
Rewrite as .
Step 2.3.14
Any root of is .
Step 2.3.15
Simplify the denominator.
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Rewrite as .
Pull terms out from under the radical, assuming positive real numbers.
Step 3
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 .
Step 4
The circle equation is .
Step 5
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