How do you complete the square for the expression $$y^2 - 6y$$ ?

To complete the square, take half of the coefficient of y (which is -6), square it (resulting in 9), and add it to the expression: $$y^2 - 6y + 9 = (y - 3)^2$$ .

What is the radius of the circle with the equation $$(x - 1)^2 + (y + 4)^2 = 36$$ ?

The radius is 6, since $$\text{r} = \text{sqrt}(36) = 6$$ .

Complete the square for the expression $$x^2 - 12x$$ .

The completed square is $$(x - 6)^2 - 36$$ .

What is the significance of the center in the equation of a circle?

The center (h, k) represents the point around which the circle is drawn, and it is the midpoint of the circle.

Write the general equation of a circle with center at (-4, 1) and radius 3.

The equation is $$(x + 4)^2 + (y - 1)^2 = 9$$ .

What does it mean to 'complete the square'?

Completing the square is a method used to convert a quadratic expression into a perfect square trinomial, making it easier to solve or graph.

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

From the equation $$(x - h)^2 + (y - k)^2 = r^2$$ , the center is (h, k).

What is the constant term that completes the square for $$y^2 + 4y$$ ?

The constant term needed is 4, since half of 4 is 2, and 2 squared is 4.

Write the equation of a circle with center at (2, -3) and radius 5.

The equation is $$(x - 2)^2 + (y + 3)^2 = 25$$ .

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

The area A of a circle is given by the formula $$A = \text{π}r^2$$ , where r is the radius.

Writing Equations of a Circle Flashcards

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the general equation of a circle?

Back

Tags

CCSS.HSG.GPE.A.1

2.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

Back

The constant term needed is 16, since half of 8 is 4, and 4 squared is 16.

Tags

CCSS.HSA-REI.B.4B

4.

FLASHCARD QUESTION

Front

Write the equation of a circle with center at (0, 0) and radius 4.

Back

Tags

CCSS.HSG.GPE.A.1

5.

FLASHCARD QUESTION

Front

Back

The center of the circle is (-3, 2).

Tags

CCSS.HSG.GPE.A.1

6.

FLASHCARD QUESTION

Front

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

Back

Tags

CCSS.HSG.GPE.A.1

7.

FLASHCARD QUESTION

Front

Back

Tags

CCSS.HSG.GPE.A.1

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