What is the radius of a circle given by the equation $$(x+3)^2 + (y-6)^2 = 25$$ ?

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

How do you determine the area of a sector of a circle?

The area of a sector is given by the formula: $$A = \frac{\theta}{360} \times \text{π}r^2$$ , where $$\theta$$ is the angle in degrees.

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

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

What does it mean for a circle to be in standard form?

A circle is in standard form when its equation is expressed as $$(x-h)^2 + (y-k)^2 = r^2$$ .

How do you find the center and radius from the equation $$x^2 + 10x + y^2 + 8y = 59$$ ?

Complete the square: Center is (-5, -4) and radius is 10.

What is the significance of the values h and k in the circle's equation?

The values h and k represent the x and y coordinates of the center of the circle.

What is the equation of a circle with diameter endpoints at (3,-4) and (-5,-4)?

The equation is $$(x+1)^2 + (y+4)^2 = 16$$ .

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

Group x and y terms, complete the square for each, and rearrange to the standard form.

What is the area of a sector with a radius of 3 yards and an angle of 90 degrees?

The area is $$A = \frac{90}{360} \times \text{π}(3^2) = \frac{1}{4} \times 9\text{π} = \frac{9\text{π}}{4} \text{ yd}^2$$ .

NC Math 3 Review: 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 complete the square for the equation of a circle?

Back

To complete the square, rearrange the equation to group x and y terms, then add and subtract the necessary constants to form perfect squares.

Tags

CCSS.HSG.GPE.A.1

3.

FLASHCARD QUESTION

Front

Back

The center is (-3, 6) after completing the square.

Tags

CCSS.HSG.GPE.A.1

4.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSG.GPE.A.1

5.

FLASHCARD QUESTION

Front

How do you find the diameter of a circle from its endpoints?

Back

6.

FLASHCARD QUESTION

Front

What is the area of a circle with radius r?

Back

Tags

CCSS.7.G.B.4

7.

FLASHCARD QUESTION

Front

What is the formula for the circumference of a circle?

Back

Tags

CCSS.7.G.B.4

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