Equation of a Circle

Review Warm-Up

​Look back at your notes and make sure you know the formulas for each circle on the right.

Central Angle

• A central angle of a circle has a vertex at the center and is formed by two radii.

• The measure of the central angle is the same as the measure of its corresponding arc of the circle.

Inscribed Angle

• An inscribed angle in a circle has a vertex on the circle and is formed by two chords.

• The measure of an inscribed angle is half the measure of its corresponding arc of the circle.

Multiple Choice

• 67.5°
• 90°
• 22.5°
• 45°

Exterior Angle

Multiple Choice

What is the measure of angle 2?

• 80
• 45
• 125
• 40

Multiple Choice

Solve for x.

• 34

• 17

• 23

• 27

Interior Angle

• An interior angle has a vertex inside the circle and is formed by two intersecting chords/secants.

• The measure of an interior angle is half the sum of its corresponding arcs.

• (arc1 + arc2)/2

Multiple Choice

What is the measure of the angle DBC?

• $$m\angle DBC=65\degree$$

• $$m\angle DBC=87.5\degree$$

• $$m\angle DBC=120\degree$$

• $$m\angle DBC=62.5\degree$$

Multiple Choice

What is the measure of angle HKI?

• 72
• 73
• 74
• 75

Take notes on ​Today's Lesson

6.4 Equation of a Circle

​

​Part 1

Equations of Circles

Objective: Identify center and radius of a circle. Write an equation of a circle from a graph, and rewrite an equation in standard form.

Circle

• A collection of all points (x, y) that are equidistant from a fixed point (h, k)

• Radius ( r ) - the distance between the center and all points (x, y) on the circle

• Center: (h, k)

Standard From of a Circle

Multiple Choice

What is the center and radius of

$$x^2+y^2=9$$  ?

• (3, 3); r = 3

• (0, 0); r = 9

• (0, 3); r = 3

• (0, 0); r = 3

Multiple Choice

What is the radius and center of

$$\left(x-9\right)^2+\left(y+3\right)^2=49$$  

• (9, -3); r = 7

• (9, 3); r = 7

• (9, -3); r = 49

• (-9, -3); r = 7

Multiple Choice

What is the center and radius of

$$\left(x+1\right)^2+\left(y+2\right)^2=10$$  

• (-1, -2); r = 10

• (-1, -2); r =  $$\sqrt{10}$$  

• (1, 2); r = 10

• (1, 2); r =  $$\sqrt{10}$$  

Multiple Choice

What is the center of the circle with equation

x² + y² = 1 ?

• (1, 1)

• (0, 0)

• (-1, -1)

Multiple Choice

What is the center of a circle with equation

(x-4)² + y² = 5 ?

• (-4, 0)

• (4, 0)

• (4, 1)

• (-4, 1)

Multiple Choice

What is the radius of a circle with equation

(x+7)² + (y-2)² = 144 ?

• 7

• 12

• 13

Multiple Choice

Write the equation of the circle with a center at (2, –4)

and a radius of 4.

• (x – 2)² + (y + 4)² = 4

• (x + 2)² + (y – 4)² = 4

• (x – 2)² + (y + 4)² = 16

• (x + 2)² + (y – 4)² = 16

Multiple Choice

Write the equation of a circle with a center at (7, 0)

and a radius of 3.

• (x - ^7)^2 + y^2 = 9

• x^2 + (y -7)^2 = 9

• (x - 7)^2 + y^2 = 3

• x^2 + (y -7)^2 = 3

Multiple Choice

What is the center of this circle?

• (2, 2)

• (2, -2)

• (0, 0)

• (-2, 2)

Multiple Choice

What is the radius of this circle?

• 2

• 6

• 3

• 5

Multiple Choice

What is the equation of this circle?

• (x+2) + (y-2) = 9

• (x+2) + (y+2) = 9

• (x+1) + (y+1) = 3

• (x+1) + (y+1) = 3

Multiple Choice

What is the equation for this circle?

• (x+1) + (y+1) = 9

• x² + y² = 9

• x + y = 9

Multiple Choice

Write the equation of the graphed circle.

• x² + (y + 3)² = 3

• x² + (y – 3)² = 3

• x² + (y + 3)² = 9

• x² + (y – 3)² = 9

Poll

Are you understanding the math concepts from this lesson today?

Take notes on ​Today's Lesson

6.4 Equation of a Circle

​

​Part 2

Sometimes Circles are not Written in the Form:

​(x-h)^2 + (y-k)^2 = r^2

​

​Examples

​1 and 2

Sometimes Circles are not Written in the Form:

​(x-h)^2 + (y-k)^2 = r^2

​

​Example 3

​Example 4: Convert the circle equation into standard form.

Multiple Choice

Convert the to standard form. x² + y² + 6x - 10y - 15 = 0

• (x + 6)² + (y - 10)² = 225

• (x + 3)² + (y - 5)² = 361

• (x + 3)² + (y - 5)² = 7

• (x + 3)² + (y - 5)² = 49

Multiple Choice

Determine the equation of the circle in standard form:
x² + y² + 4x + 6y - 36 = 0

• (x+2)² + (y+3)² = 49
• (x+2)² + (y+3)² = 13
• (x-2)² + (y-3)² = 49
• (x-2)² + (y-3)² = 13

Multiple Choice

Determine the equation of the circle in standard form: x² + y² + 6x - 12y + 20 = 0

• (x-3)² + (y+6)² = 25
• (x+3)² + (y-6)² = 25
• (x-3)² + (y+6)² = 45
• (x+3)² + (y-6)² = 5

Multiple Choice

Convert the equation of the circle from standard to general.

• A

• B

• C

• D

Multiple Choice

Determine the center and radius: x² + y² + 14x - 2y = -1

• center= (-7,2) radius= 3
• center= (-7,1) radius= 7
• center= (-4,1) radius= 5

Multiple Choice

Determine the center and radius:
x² + y² - 10x + 8y -8 = 0

• C = (5,-4) r = 7
• C = (-5,4) r = 7
• C = (-4,5) r = 49
• C = (5,-4) r = 49

Multiple Choice

What is the center of

$$x^2+y^2+6x-8y-11=0$$  

• (6, 0)

• (-3, 4)

• (4, -3)

• (3, 4)

Multiple Choice

What is the radius of

$$x^2+y^2-2x+6y-10=0$$  

• $$20$$  

• $$0$$  

• $$\sqrt{10}$$  

• $$\sqrt{20}$$  

Multiple Choice

What is the center and radius given the equation, x² + y² + 8x - 2y - 64 = 0?

• Center: (-4, 1), Radius: 9

• Center: (4,1), Radius: 8

• Center: (1,-4), Radius: 64

• Center: (-4, 1), Radius: 81

Poll

How are you feeling about being able to answer questions about equations of circles?