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Understanding the Equation of a Circle

Understanding the Equation of a Circle

Assessment

Interactive Video

Mathematics

7th - 10th Grade

Practice Problem

Hard

CCSS
HSG.GPE.A.1

Standards-aligned

Created by

Lucas Foster

FREE Resource

Standards-aligned

CCSS.HSG.GPE.A.1
This video introduces the equation of a circle, explaining how to derive it using the center and radius. It provides examples with circles centered at (0,0), (5,2), and (-2,3), demonstrating how to write their equations. The video also shows how to verify if a point lies on a circle by substituting the point's coordinates into the circle's equation.

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10 questions

Show all answers

1.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the general form of the equation of a circle?

(x + a)^2 + (y + b)^2 = r^2

x^2 + y^2 = 2r

(x - a)^2 + (y - b)^2 = r^2

x^2 + y^2 = r^2

Tags

CCSS.HSG.GPE.A.1

2.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

In the equation (x - a)^2 + (y - b)^2 = r^2, what do 'a' and 'b' represent?

The coordinates of a point on the circle

The coordinates of the center of the circle

The diameter of the circle

The radius of the circle

Tags

CCSS.HSG.GPE.A.1

3.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What does the term (x - a)^2 + (y - b)^2 = r^2 represent in geometry?

A line

A parabola

A circle

An ellipse

Tags

CCSS.HSG.GPE.A.1

4.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

If a circle is centered at (0, 0) with a radius of 5, what is its equation?

(x + 5)^2 + (y + 5)^2 = 25

x^2 + y^2 = 5

(x - 5)^2 + (y - 5)^2 = 25

x^2 + y^2 = 25

Tags

CCSS.HSG.GPE.A.1

5.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

How do you modify the circle equation for a center at (5, 2)?

(x + 5)^2 + (y + 2)^2 = r^2

(x - 5)^2 + (y - 2)^2 = r^2

(x + 2)^2 + (y + 5)^2 = r^2

(x - 2)^2 + (y - 5)^2 = r^2

Tags

CCSS.HSG.GPE.A.1

6.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the radius of a circle if its equation is (x - 5)^2 + (y - 2)^2 = 4?

16

8

4

2

Tags

CCSS.HSG.GPE.A.1

7.

MULTIPLE CHOICE QUESTION

30 sec • 1 pt

What is the equation of a circle with center (-2, 3) and radius 1?

(x - 2)^2 + (y + 3)^2 = 1

(x - 2)^2 + (y - 3)^2 = 1

(x + 2)^2 + (y + 3)^2 = 1

(x + 2)^2 + (y - 3)^2 = 1

Tags

CCSS.HSG.GPE.A.1

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