Convert the equation $$x^2 + y^2 - 4x + 6y - 12 = 0$$ to standard form.

The standard form is $$(x - 2)^2 + (y + 3)^2 = 25$$ .

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

From the standard form $$(x - h)^2 + (y - k)^2 = r^2$$ , the radius r can be found by taking the square root of the right side: $$r = \text{sqrt}(r^2)$$ .

What is the relationship between the center and the radius in a circle?

The center of a circle is a fixed point from which all points on the circle are equidistant, with that distance being the radius.

Write the equation of a circle with center (3, -2) and radius 5.

The equation is $$(x - 3)^2 + (y + 2)^2 = 25$$ .

What is the effect of changing the center of a circle on its equation?

Changing the center (h, k) in the equation $$(x - h)^2 + (y - k)^2 = r^2$$ shifts the circle's position in the coordinate plane without changing its size.

How do you convert from general form to standard form for a circle?

To convert from general form $$Ax^2 + Ay^2 + Bx + Cy + D = 0$$ to standard form, complete the square for the x and y terms.

What is the significance of the constant term in the equation of a circle?

The constant term in the equation of a circle affects the size of the circle; specifically, it relates to the radius when the equation is in standard form.

How can you identify the radius from the equation $$(x + 4)^2 + (y - 3)^2 = 16$$ ?

The radius is found by taking the square root of the right side: $$r = \text{sqrt}(16) = 4$$ .

What does it mean if the radius squared is negative in a circle's equation?

If the radius squared is negative, it indicates that the equation does not represent a real circle, as a circle cannot have a negative radius.

Unit 9.1: Conics: Circles 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

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

Back

Tags

CCSS.HSG.GPE.A.1

3.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSG.GPE.A.1

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSG.GPE.A.1

5.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSG.GPE.A.1

6.

FLASHCARD QUESTION

Front

How do you determine if a given equation represents a circle?

Back

Tags

CCSS.HSG.GPE.A.1

7.

FLASHCARD QUESTION

Front

What is the diameter of a circle?

Back

The diameter of a circle is twice the radius and is the longest distance across the circle, passing through the center.

Tags

CCSS.HSG.C.A.2

Create a free account and access millions of resources

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

15 questions

Practice 3 FFA Basics

Flashcard

•

9th - 12th Grade

15 questions

What is the Limit?

Flashcard

•

11th Grade

10 questions

Strategies to Avoid Communication Breakdown

Flashcard

•

11th - 12th Grade

16 questions

MODALS IN THE PAST

Flashcard

•

9th - 12th Grade

10 questions

Marketing Mix - Place and Distribution

Flashcard

•

10th Grade - University

12 questions

DNA Replication and Protein Synthesis

Flashcard

•

9th - 12th Grade

14 questions

History of Periodic Table of Elements

Flashcard

•

8th - 11th Grade

Popular Resources on Wayground

10 questions

Forest Self-Management

Lesson

•

1st - 5th Grade

25 questions

Multiplication Facts

Quiz

•

5th Grade

30 questions

Thanksgiving Trivia

Quiz

•

9th - 12th Grade

30 questions

Thanksgiving Trivia

Quiz

•

6th Grade

11 questions

Would You Rather - Thanksgiving

Lesson

•

KG - 12th Grade

48 questions

The Eagle Way

Quiz

•

6th Grade

10 questions

Identifying equations

Quiz

•

KG - University

10 questions

Thanksgiving

Lesson

•

5th - 7th Grade

Discover more resources for Mathematics

10 questions

Identifying equations

Quiz

•

KG - University

20 questions

Pythagorean Theorem and Their Converse

Quiz

•

8th - 9th Grade

20 questions

Is it a Function?

Quiz

•

8th - 9th Grade

18 questions

Scatterplot Associations

Quiz

•

7th - 9th Grade

26 questions

Intro to Exponential Functions

Quiz

•

9th Grade

8 questions

211 - Write Equation Given Two Points

Quiz

•

9th Grade

16 questions

Solving Systems Review

Quiz

•

9th Grade

18 questions

Triangle Similarity Review

Quiz

•

9th - 12th Grade