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

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

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

The general form is $$Ax^2 + Ay^2 + Bx + Cy + D = 0$$ , where A is not equal to 0.

If a circle has a center at (3, -4) and a radius of 2, what is its equation?

The equation is $$(x - 3)^2 + (y + 4)^2 = 4$$ .

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 standard form by transforming it into a perfect square trinomial.

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

The radius determines the size of the circle and is the distance from the center to any point on the circle.

Write the equation of a circle with center (5, 5) and radius 3.

The equation is $$(x - 5)^2 + (y - 5)^2 = 9$$ .

How can you identify the center and radius from the equation $$(x - 4)^2 + (y + 1)^2 = 25$$ ?

The center is (4, -1) and the radius is 5.

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

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

If the equation of a circle is given as $$x^2 + y^2 - 6x + 8y + 9 = 0$$ , how do you find its center and radius?

First, rearrange to complete the square: center is (3, -4) and radius is 5.

equation of a circle

Flashcard

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Mathematics

•

10th Grade

•

Practice Problem

•

Hard

•

CCSS

HSG.GPE.A.1, HSG.C.A.2

Standards-aligned

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FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSG.GPE.A.1

FLASHCARD QUESTION

Front

What does the center of a circle represent in its equation?

Back

Tags

CCSS.HSG.GPE.A.1

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSG.GPE.A.1

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSG.GPE.A.1

FLASHCARD QUESTION

Front

Write the equation of a circle with center (0, 0) and radius 5.

Back

Tags

CCSS.HSG.GPE.A.1

FLASHCARD QUESTION

Front

Back

The center is (-1, 2).

Tags

CCSS.HSG.GPE.A.1

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

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