# Precalculus Examples

,

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 .

Use the distance formula to determine the distance between the two points.

Substitute the actual values of the points into the distance formula.

Simplify.

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 .

Combine.

Multiply by to get .

Combine the numerators over the common denominator.

Simplify the numerator.

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 .

Combine.

Multiply by to get .

Combine the numerators over the common denominator.

Simplify the numerator.

Multiply by to get .

Add and .

Rewrite as .

Simplify the denominator.

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 .