What is the radius of a circle with the equation $$(x - 2)^2 + (y + 3)^2 = 16$$ ?

The radius is 4, since $$r^2 = 16$$ and $$r = \text{sqrt}(16) = 4$$ .

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

The general form is $$Ax^2 + Ay^2 + Bx + Cy + D = 0$$ , where A is not equal to 0.

If a circle has a center at (3, -4) and a radius of 2, what is its equation?

The equation is $$(x - 3)^2 + (y + 4)^2 = 4$$ .

What does the term 'completing the square' mean in the context of circles?

Completing the square is a method used to rewrite a quadratic equation in standard form by transforming it into a perfect square trinomial.

What is the significance of the radius in the context of a circle?

The radius determines the size of the circle and is the distance from the center to any point on the circle.

Write the equation of a circle with center (5, 5) and radius 3.

The equation is $$(x - 5)^2 + (y - 5)^2 = 9$$ .

How can you identify the center and radius from the equation $$(x - 4)^2 + (y + 1)^2 = 25$$ ?

The center is (4, -1) and the radius is 5.

What is the relationship between the radius and the diameter of a circle?

The diameter is twice the radius: $$d = 2r$$ .

If the equation of a circle is given as $$x^2 + y^2 - 6x + 8y + 9 = 0$$ , how do you find its center and radius?

First, rearrange to complete the square: center is (3, -4) and radius is 5.

equation of a circle Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSG.GPE.A.1

2.

FLASHCARD QUESTION

Front

What does the center of a circle represent in its equation?

Back

Tags

CCSS.HSG.GPE.A.1

3.

FLASHCARD QUESTION

Front

How do you find the radius of a circle from its equation?

Back

Tags

CCSS.HSG.GPE.A.1

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSG.GPE.A.1

5.

FLASHCARD QUESTION

Front

Write the equation of a circle with center (0, 0) and radius 5.

Back

Tags

CCSS.HSG.GPE.A.1

6.

FLASHCARD QUESTION

Front

Back

The center is (-1, 2).

Tags

CCSS.HSG.GPE.A.1

7.

FLASHCARD QUESTION

Front

How do you convert the general form of a circle's equation to standard form?

Back

Tags

CCSS.HSG.GPE.A.1

Access all questions and much more by creating a free account

Create resources

Host any resource

Get auto-graded reports

Continue with Google

Continue with Email

Continue with Classlink

Continue with Clever

or continue with

Microsoft

Apple

Others

Already have an account?

Similar Resources on Wayground

8 questions

Accounting Concepts

Flashcard

•

11th Grade

10 questions

Geometry FD Module 3 Vocab

Flashcard

•

10th Grade

15 questions

Urban Heat Islands

Flashcard

•

9th Grade

15 questions

Unit II Test Review Bio A (Ch. 3-5)

Flashcard

•

9th - 11th Grade

10 questions

Printing Press

Flashcard

•

9th - 12th Grade

8 questions

MATHEMATICS 10 - Graph of Polynomial Functions PART 1

Flashcard

•

10th Grade

12 questions

Trennbare Verben

Flashcard

•

KG

15 questions

Stamped Chapter 1: Understanding Racism

Flashcard

•

10th Grade

Popular Resources on Wayground

15 questions

Fractions on a Number Line

Quiz

•

3rd Grade

20 questions

Equivalent Fractions

Quiz

•

3rd Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

$fractions$

22 questions

fractions

Quiz

•

3rd Grade

20 questions

Main Idea and Details

Quiz

•

5th Grade

20 questions

Context Clues

Quiz

•

6th Grade

15 questions

Equivalent Fractions

Quiz

•

4th Grade

20 questions

Figurative Language Review

Quiz

•

6th Grade

Discover more resources for Mathematics

25 questions

Complementary and Supplementary Angles

Quiz

•

7th - 10th Grade

12 questions

Add and Subtract Polynomials

Quiz

•

9th - 12th Grade

13 questions

Model Exponential Growth and Decay Scenarios

Quiz

•

9th - 12th Grade

27 questions

7.2.3 Quadrilateral Properties

Quiz

•

9th - 12th Grade

16 questions

Converting Improper Fractions to Mixed Numbers

Quiz

•

4th - 10th Grade

10 questions

Simplifying Expressions by Combining Like Terms

Interactive video

•

6th - 10th Grade

10 questions

Simplifying Expressions with the Distributive Property

Interactive video

•

6th - 10th Grade

10 questions

Key Features of Quadratic Functions

Interactive video

•

8th - 12th Grade