If the equation of a circle is $$x^2 + y^2 = 25$$ , what is the radius?

The radius is 5, since $$r^2 = 25$$ and $$r = \sqrt{25} = 5$$ .

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

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

If a circle has a center at (0, 0) and a radius of 10, what is its equation?

The equation is $$x^2 + y^2 = 100$$ .

What is the significance of the value on the right side of the equation $$(x-h)^2 + (y-k)^2 = r^2$$ ?

The value on the right side, r^2, represents the square of the radius of the circle.

For the equation $$(x-2)^2 + (y+3)^2 = 25$$ , what is the radius?

The radius is 5, since $$r^2 = 25$$ .

What is the equation of a circle with center (4, -2) and radius 6?

The equation is $$(x-4)^2 + (y+2)^2 = 36$$ .

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; equal to r^2, it's on; greater than r^2, it's outside.

What is the radius of the circle represented by the equation $$x^2 + y^2 - 8x + 6y = 0$$ ?

The radius is 5, after completing the square.

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

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

Equations of a Circle Flashcards

Student preview

14 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

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

Back

Tags

CCSS.HSG.GPE.A.1

3.

FLASHCARD QUESTION

Front

What does the center 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

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

Back

The center is (-5, 1).

Tags

CCSS.HSG.GPE.A.1

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