# Precalculus Examples

,

Step 1

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

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

Simplify.

Step 2.3.1

Subtract from .

Step 2.3.2

Raise to the power of .

Step 2.3.3

To write as a fraction with a common denominator, multiply by .

Step 2.3.4

Combine and .

Step 2.3.5

Combine the numerators over the common denominator.

Step 2.3.6

Simplify the numerator.

Step 2.3.6.1

Multiply by .

Step 2.3.6.2

Subtract from .

Step 2.3.7

Move the negative in front of the fraction.

Step 2.3.8

Use the power rule to distribute the exponent.

Step 2.3.8.1

Apply the product rule to .

Step 2.3.8.2

Apply the product rule to .

Step 2.3.9

Raise to the power of .

Step 2.3.10

Multiply by .

Step 2.3.11

Raise to the power of .

Step 2.3.12

Raise to the power of .

Step 2.3.13

Write as a fraction with a common denominator.

Step 2.3.14

Combine the numerators over the common denominator.

Step 2.3.15

Add and .

Step 2.3.16

Rewrite as .

Step 2.3.17

Simplify the denominator.

Step 2.3.17.1

Rewrite as .

Step 2.3.17.2

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

Simplify the circle equation.

Step 6