What is the radius of a circle given the equation $$(x - 4)^2 + (y - 3)^2 = 25$$ ?

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

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 the radius from the equation of a circle in standard form?

The radius is the square root of the constant on the right side of the equation. For example, in $$(x - h)^2 + (y - k)^2 = r^2$$ , the radius is $$r = \text{sqrt}(r^2)$$ .

What is the significance of the equation $$x^2 + y^2 = r^2$$ ?

This equation represents a circle centered at the origin (0, 0) with radius r.

How do you find the coordinates of the center from the equation $$x^2 + y^2 + 4x + 6y - 36 = 0$$ ?

First, rearrange to complete the square: $$(x + 2)^2 + (y + 3)^2 = 49$$ . The center is (-2, -3).

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

The area of a circle increases with the square of the radius, as given by the formula $$A = \text{pi} r^2$$ .

If a circle has an area of 78.5 square units, what is the radius?

Using the area formula, $$A = \text{pi} r^2$$ , we find $$r = \text{sqrt}(A/\text{pi}) = \text{sqrt}(78.5/\text{pi})$$ .

What is the formula for the circumference of a circle?

The circumference is given by the formula $$C = 2\text{pi} r$$ .

How do you find the radius if the diameter of a circle is known?

The radius is half of the diameter, so $$r = \frac{d}{2}$$ .

Equations of a circle review 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

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

Back

Tags

CCSS.HSG.GPE.A.1

3.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSG.GPE.A.1

4.

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

5.

FLASHCARD QUESTION

Front

What is the area of a circle with radius 10 units?

Back

Tags

CCSS.7.G.B.4

6.

FLASHCARD QUESTION

Front

What is the diameter of a circle if the radius is 6 units?

Back

Tags

CCSS.7.G.B.4

7.

FLASHCARD QUESTION

Front

Back

The center is (-7, -3).

Tags

CCSS.HSG.GPE.A.1

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