What is the radius of the circle given by the equation $$(x - 1)^2 + (y + 2)^2 = 9$$ ?

The radius is 3, since $$\text{sqrt}(9) = 3$$ .

What is the distance between the center of the circle $$(x - 1)^2 + (y - 2)^2 = 25$$ and the point (4, 6)?

The distance is 5, calculated using the distance formula: $$\text{sqrt}((4 - 1)^2 + (6 - 2)^2) = 5$$ .

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 the form of a perfect square trinomial, which helps in identifying the center and radius of the circle.

How do you determine if a point lies inside, on, or outside a circle?

Substitute the point (x, y) into the circle's equation. If the result is less than r^2, it's inside; if equal, it's on; if greater, it's outside.

What is the equation of a circle with center (-2, 5) and radius $$\text{sqrt}(10)$$ ?

The equation is $$(x + 2)^2 + (y - 5)^2 = 10$$ .

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

The radius determines the size of the circle; a larger radius means a larger circle.

What is the equation of a circle with center (1, 2) and radius 5?

The equation is $$(x - 1)^2 + (y - 2)^2 = 25$$ .

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 radius of a circle from its equation?

Back

Tags

CCSS.HSG.GPE.A.1

3.

FLASHCARD QUESTION

Front

Back

The center of the circle is (-3, 4).

Tags

CCSS.HSG.GPE.A.1

4.

FLASHCARD QUESTION

Front

If the radius of a circle is 5, what is the equation of the circle centered at (2, -1)?

Back

Tags

CCSS.HSG.GPE.A.1

5.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSG.GPE.A.1

6.

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

7.

FLASHCARD QUESTION

Front

What is the equation of a circle with center (0, 0) and radius 4?

Back

Tags

CCSS.HSG.GPE.A.1

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