Midpoint formula:

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COORDINATE PLANE FORMULAS

• Midpoint formula

1. (- 3, 2) and (7, - 8)
2. (2, 5) and (4, 10)

1. (1, 2) and (4, 6)
2. (-2, -5) and (3, 7)

• Distance formula

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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)
If all 3 points are on the circle, then all
distances are equal!! d1 d2 d3
GIVEN POINT
CENTER
EQUIDISTANT
RADIUS
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CIRCLE FORMULA Standard Form
(h, k)
Center
r
Radius

• Derive Formula Distance

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PRACTICE 1 Interpret Equation of a Circle

• IDENTIFY the center and radius in the equation.
• a.
• Center _________ Radius ________
• b.
• Center _________ Radius ________
• c.
• Center _________ Radius ________

(2, -5)
(4, 7)
(-1, -3)
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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)
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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
xs and ys (Add Both to Right Side)
Step 1
Step 2
Step 3
Center (-4, 6) Radius 9
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PRACTICE 4 Writing Circles in Standard Form
Write in standard form, find the radius and
center. Sketch a graph
A
B
Center
(3, 0)
Center
(2, -4)
Radius
r 4
Radius
10
PRACTICE 4 Continued
Write in standard form, find the radius and
center. Sketch a Graph.
D
C
Center
(3, -5)
Radius
Center
( -3/2, 0)
Radius
r 2
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PRACTICE 4 Continued
Write in standard form, find the radius and
center.
F
E
(-3, -4)
(5, -8)
Center
Center
r 4
r 5
Radius
Radius
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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.
B Center (3, 5) tangent to y-axis
A Center (-4, -3) Tangent to x-axis