Equation of a Circle

All Things Circles &

Equation of a Circle

​Dr. Tom Giles

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.

Fill in the Blanks

What is x?

Fill in the Blanks

Solve for x. Just type in the numeric value.

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.

Fill in the Blanks

Just type in the numeric value.

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.

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

Fill in the Blanks

Determine the Radius of the following equation of a circle. $x^2+y^2-12x+16y=-75$  

Only type the number

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?