# Distance and Midipoint Formula; Circle

**Objectives:
**1. To find the distance between two points

2. To find the midpoint of a line segment

3. To write the standard form of a circle’s equation

4. To give the center and radius of a circle whose

equation is in standard form

5. To convert the general form of a circle’s equation to

standard form

**Objective 1: To find the distance between two points**

The distance Formula

Given two points P

_{1}(x

_{1},y

_{1}) and P

_{2}(x

_{2},y

_{2})

Example: Find the distance between (-4, -1) and (2, - 3).

**Objective 2: To find the midpoint of a line segment
**Finding the midpoint

Formula :

Find the midpoint of the line segment with endpoints

(-4,-1) and (2, - 3)

**Objective 3: To write the standard form of a circle’s
equation**

Circle:

A circle is the set of all points in a plane that are

equidistant from a fixed point called the center. The fixed

distance from the circle’s center is called the radius.

Find the formula of a circle whose center is (h, k) and

radius is r.

The equation of a circle whose center is at the origin and

radius r is x^{2} + y^{2} = r^{2}.

Write the standard form of the equation of the circle with

center at (0,0) and the radius is 4. Graph the circle on the

board.

Equation: x^{2} + y^{2} = 16.

Write the standard form of the equation of a circle with

center (-2, 1) and radius 2. Graph circle on the board.

Equation:

**Objective 4: To give the center and radius of a circle
whose equation is in standard form**

Give the center and radius of a circle whose equation is

(x + 4)

^{2}+ (y + 5)

^{2}= 36.

The center is (-4,-5) and the radius is 6.

**Objective 5:**

To convert the general form of a circle’s equation to

standard form

To convert the general form of a circle’s equation to

standard form

The general form of the equation of a circle is

x

^{2}+ y

^{2}Dx + Ey + F= 0

Standard Form: (x - h)

^{2}+ (y – k)

^{2}= r

^{2}

Express x

^{2}+ y

^{2}+8x + 4y + 16= 0 in standard form and

find the center and the radius.

Center: (-4,-2) and radius = 2

Express x^{2} + y^{2} - 6y - 7= 0 in standard form and find the

center and the radius.

Center: (0, 3) and radius is 4

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