1. Midpoint formula: Distance formula: (x 1, y 1 ) (x 2, y 2 ) 1)(- 3, 2) and (7, - 8) 2)(2, 5) and (4, 10) 1)(1, 2) and (4, 6) 2)(-2, -5) and (3, 7) COORDINATE PLANE FORMULAS :

2. CIRCLE: The set of all points that are equidistant from a given point. GIVEN POINT:CENTER EQUIDISTANT: RADIUS (x 1, y 1 ) (x 2, y 2 ) (x 3, y 3 ) d1d1 d2d2 d3d3 (x, y) Distance #1: (x 1, y 1 ) Distance #2 : (x 2, y 2 ) Distance #3: (x 3, y 3 ) If all 3 points are on the circle, then all distances are equal!! d 1 = d 2 = d 3

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

4. 1.IDENTIFY the center and radius in the equation. a. Center: _________Radius: ________ b. Center: _________Radius: ________ c. Center: _________Radius: ________ PRACTICE #1: Interpret Equation of a Circle (2, -5) (4, 7) (-1, -3)

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

6. 4. (-1, 7) and (5, -1) PRACTICE #3: Write the equation of the circle given the endpoints of a diameter. 5. (-3, 4) and (-7, -6) Center:(2, 3) Center:(-5, -1)

7. 6. (-3, -5) and (6, 2) PRACTICE #3 : Continued 7. (4, 8) and (4, -2) Center:(4, 3) Center:(1.5, -1.5)

8. HOW TO: Writing Circles in standard form Center: (-4, 6) Radius: 9 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:

9. PRACTICE #4: Writing Circles in Standard Form [A] Write in standard form, find the radius and center. Sketch a graph [B] Center: (3, 0) Radius: r = 4 Center: (2, -4) Radius:

10. PRACTICE #4: Continued [C] Write in standard form, find the radius and center. Sketch a Graph. [D] Center: ( -3/2, 0) Radius: r = 2 Center: (3, -5) Radius:

11. [E] Center: (-3, -4) Radius: r = 4 PRACTICE #4: Continued Write in standard form, find the radius and center. [F] Center: (5, -8) Radius: r = 5

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