3.3 Equation of a Circle Day 1

3.3 Equation of a Circle

By Lilibeth Villaran

Learning Targets

I can ​

Lesson 3: Equation of a Circle

• Illustrate the center-radius form of the equation of a circle

• Determine the center and radius of a circle given its equation and vice versa

• solve problem involving circle​

Open Ended

What makes a circle unique?

Think about the shape and properties of a circle.

A set of points that is equidistant from a fixed point called the center.

Definition

Circle

Lesson 3: Equation of a Circle

Standard Form of a Circle​

Lesson 3: Equation of a Circle

​Center -Radius Form

Example 1. What is the standard form of the equation of a circle?

Lesson 3: Equation of a Circle

Identify the center and radius of the given circle.

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Example 1. What is the standard form of the equation of a circle?

Lesson 3: Equation of a Circle

Example 2. What is the standard form of the equation of a circle?

Lesson 3: Equation of a Circle

Let's play!

​Lesson 3: Equation of a Circle

Multiple Choice

What is the standard form of the equation of the circle whose center is at (5, 6) and the radius is 4?

• $$\left(x+5\right)^2+\left(x+6\right)^2=16$$  

• $$\left(x-5\right)^2+\left(y-6\right)^2=16$$  

• $$\left(x-5\right)^2+\left(y-6\right)^2=4$$  

• $$\left(x+5\right)^2+\left(x+6\right)^2=4$$  

Multiple Choice

What is the standard equation of a circle whose center is at (-3,4) and the radius is 7?

• $$\left(x+3\right)^2+\left(y-4\right)^2=49$$  

• $$\left(x-3\right)^2+\left(y+4\right)^2=49$$  

• $$\left(x-3\right)^2+\left(y+4\right)^2=7$$  

• $$\left(x+3\right)^2+\left(y-4\right)^{2\ }=7$$  

Multiple Choice

What is the center-radius form of a circle with a radius of 12 and center at (-3, -5)?

• $$\left(x-3\right)^2+\left(x-5\right)^2=12$$  

• $$\left(x-3\right)^2+\left(y-5\right)^2=144$$  

• $$\left(x+3\right)^{2\ }+\left(x+5\right)^2=144$$  

• $$\left(x+3\right)^2+\left(y+5\right)^2=12$$  

Multiple Choice

Write the standard form of the equation of the circle with radius of $$\sqrt[]{6}$$  and center at (8, 0).

• $$\left(x-8\right)^2+y^2=6$$  

• $$\left(x-8\right)^2+y^2=36$$  

• $$\left(x-8\right)^2+y=6$$  

• $$\left(x-8\right)^2+y^2=\sqrt[]{6}$$  

Multiple Choice

What is the center-radius form of a circle with a diameter of 20 units and a center at (-1, 1)?

• $$\left(x+1\right)^2+\left(y-1\right)^2=400$$  

• $$\left(x-1\right)^2+\left(y+1\right)^2=400$$  

• $$\left(x-1\right)^2+\left(y+1\right)^2=100$$  

• $$\left(x+1\right)^2+\left(y-1\right)^2=100$$  

You did great!

Lesson 3: Equation of a Circle

Finding the center and radius of a circle given the equation

Lesson 3: Equation of a Circle

center (h,k)

radius

Lesson 3: Equation of a Circle

center (h,k)

radius

Lesson 3: Equation of a Circle

center (h,k)

radius

Lesson 3: Equation of a Circle

Let's have a drill!

Lesson 3: Equation of a Circle

Multiple Choice

What is the center and radius of a circle with equation of $$\left(x-6\right)^2+\left(y+1\right)^2=81$$  ?

• C(-6, 1) and r= 81

• C(-6,1) and r=9

• C (6,-1) and r=9

• C(6, -1) and r=81

Multiple Choice

What is the radius and center of a circle with an equation of $$x^2\ +\ y^2=5$$  

• C(1,1) and r=5

• C(0,0) and r= $$\sqrt[]{5}$$  

• C(0,0) and r= 5

• C(0,0) and r = 25

Multiple Choice

Find the radius and center of a circle with equation of $$x^2+\left(y+4\right)^2=10$$  

• C(0, 4) and r= $$\sqrt[]{10}$$  

• C(0,-4) and r=100

• C(1, 4) and r= 10

• C (0, -4) and r= $$\sqrt[]{10}$$  

You did well!

The next questions will be tricky.​ Let's go!

Lesson 3: Equation of a Circle

Multiple Choice

Write the equation of the circle in standard form.

• $$\left(x-1\right)^2+\left(y-1\right)^2=5$$  

• $$\left(x-1\right)^2+\left(y-1\right)^2=16$$  

• $$\left(x-1\right)^2+\left(y-1\right)^2=25$$  

• $$\left(x+1\right)^2+\left(y+1\right)^2=4$$  

Multiple Choice

Find the center-radius form of the equation of the circle.

• $$\left(x+2\right)^2+\left(y-1\right)^2=8$$  

• $$\left(x-2\right)^2+\left(y-1\right)^2=64$$  

• $$\left(x-2\right)^2+\left(y+1\right)^2=64$$  

• $$\left(x+2\right)^2+\left(y-1\right)^2=64$$  

Multiple Choice

What is the equation of the circle in standard form?

• $$x^2+y^2=15$$  

• $$x^2+y^2=125$$  

• $$x^2+y^2=225$$  

• $$x^2+y^2=0$$  

Great work!

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Lesson 3: Equation of a Circle

Solving problems involving circle

​Some text here about the topic of discussion.

​Some text here about the topic of discussion.

Write an equation of a circle whose center is at (4, 3) and passing through (1, 6).

​Some text here about the topic of discussion.

Write an equation of a circle whose center is at (4, 3) and passing through (1, 6).

Write an equation of a circle whose center is at (-5, 3) and passing through (-2, -1).

Some text here about the topic of discussion

Write an equation of a circle whose center is at (-5, 3) and passing through (-2, -1).

Some text here about the topic of discussion

ALA Activities

Please answer and submit in the class notebook.

Lesson 3: Equation of a Circle

• Module 3 Activity 7

• Module 3 Activity 8

• Module 3 Activity 9

  Due on April 8, 2022

Thank you!

Lesson 3: Equation of a Circle