1. COORDINATE PLANE FORMULAS:
Midpoint formula:
(x1, y1)
(x2, y2)
(- 3, 2) and (7, - 8)
(2, 5) and (4, 10)
(1, 2) and (4, 6)
(-2, -5) and (3, 7)
Distance formula:

2. CIRCLE: The set of all points that are equidistant from a given point.
Distance #1: (x1, y1)
(x1, y1) d1
Distance #2 : (x2, y2)
(x, y) d2 d3
(x2, y2)
Distance #3: (x3, y3)
(x3, y3)
GIVEN POINT:
EQUIDISTANT:

3. Derive Formula: Distance
CIRCLE FORMULA: Standard Form
Center:
(x, y)
(h, k)
Radius:
Derive Formula: Distance

4. PRACTICE #1: Interpret Equation of a Circle
IDENTIFY the center and radius in the equation. a.
Center: _________ Radius: ________ b. c.

5. PRACTICE #2: Write the Equation of a Circle
2. Write an equation of the circle with a center (-1, 3) and radius of 6.
3. Write the equation of the circle pictured to the right

6. Write the equation of the circle given the endpoints of a diameter.
PRACTICE #3:
4. (-1, 7) and (5, -1)
5. (-3, 4) and (-7, -6)

7. PRACTICE #3 : Continued
6. (-3, -5) and (6, 2)
7. (4, 8) and (4, -2)

8. HOW TO: Writing Circles in standard form
Step #1: Group x and y terms separately together
Step #2: Move the constant term to the opposite side
Step #3: Complete the square for x’s and y’s (Add Both to Right Side)
Step #1:
Step #2:
Step #3:
Standard Form:
Center: (-4, 6) Radius: 9

9. PRACTICE #4: Writing Circles in Standard Form
Write in standard form, find the radius and center.
Sketch a graph
[A]
[B]

10. PRACTICE #4: Continued
Write in standard form, find the radius and center.
Sketch a Graph.
[D]
[C]

11. PRACTICE #4: Continued
Write in standard form, find the radius and center.
[E]
[F]

12. PRACTICE #5: Equations given the a Tangent
TANGENT: A line intersecting at exactly one point with another curve.
Additional Fact: Tangents are perpendicular to the curve.
Write the equation of the circle given its tangency to an axis.
[A] Center: (-4, -3)
Tangent to x-axis
[B] Center: (3, 5)
tangent to y-axis