What is the radius of the circle given by the equation $$(x + 2)^2 + (y - 5)^2 = 25$$ ?

The radius is 5, since $$r^2 = 25$$ , thus $$r = \text{sqrt}(25) = 5$$ .

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

To determine the radius from the equation $$(x - h)^2 + (y - k)^2 = r^2$$ , take the square root of the right side, r = $$\text{sqrt}(r^2)$$ .

What is the significance of the number on the right side of the circle's equation?

The number on the right side of the equation $$(x - h)^2 + (y - k)^2 = r^2$$ represents the square of the radius.

If the equation of a circle is $$(x - 1)^2 + (y - 3)^2 = 16$$ , what is the radius?

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

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

The general form of the equation of a circle is $$x^2 + y^2 + Dx + Ey + F = 0$$ .

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

To convert from general form to standard form, complete the square for the x and y terms.

What is the distance between the center and a point on the circumference of a circle?

The distance is equal to the radius of the circle.

What does it mean if the radius of a circle is zero?

If the radius is zero, the circle is reduced to a single point, which is the center.

How do you graph a circle given its equation?

To graph a circle, identify the center (h, k) and plot points at a distance r from the center in all directions.

Conics- Circles Flashcards

Student preview

15 questions

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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 radius of a circle represent?

Back

The radius of a circle is the distance from the center of the circle to any point on its circumference.

3.

FLASHCARD QUESTION

Front

How do you find the center 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

Back

The center is (-2, -3).

Tags

CCSS.HSG.GPE.A.1

6.

FLASHCARD QUESTION

Front

Write the equation of a circle with center (3, 4) and radius 2.

Back

Tags

CCSS.HSG.GPE.A.1

7.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSG.GPE.A.1

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