How do you complete the square for the expression $$x^2 - 12x$$ ?

To complete the square, take half of the coefficient of x, square it, and adjust the equation: $$(x-6)^2 - 36$$ .

What is the radius of the circle in the equation $$(x-5)^2 + (y-4)^2 = 16$$ ?

The radius of the circle is $$\text{r} = \text{sqrt}(16) = 4$$ .

How do you convert the equation $$x^2 + y^2 - 10x + 8y + 9 = 0$$ to standard form?

Complete the square for x and y: $$(x-5)^2 + (y-4)^2 = 16$$ .

What is the significance of the point (h, k) in the circle equation?

The point (h, k) represents the center of the circle.

How do you find the radius from the equation $$(x-h)^2 + (y-k)^2 = r^2$$ ?

The radius is found by taking the square root of r^2: $$r = \text{sqrt}(r^2)$$ .

What is the first step in converting a general form equation of a circle to standard form?

The first step is to group the x and y terms and move the constant to the other side.

What is the equation of a circle with center at (-4, 1) and radius 3?

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

What is the process of completing the square?

Completing the square involves rewriting a quadratic expression in the form of a perfect square trinomial.

What is the relationship between the coefficients in the general form of a circle's equation and its center and radius?

The coefficients determine the center (h, k) and the radius r when the equation is rewritten in standard form.

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

The center is (-2, -1) and the radius is $$\text{r} = \text{sqrt}(25) = 5$$ .

What is the importance 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.

Writing Equations of a Circle Flashcards

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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

Back

Tags

CCSS.HSA-REI.B.4B

3.

FLASHCARD QUESTION

Front

Back

The center of the circle is at the point (-4, 1).

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

What is the general equation of a circle with center at (2, -3) and radius 5?

Back

Tags

CCSS.HSG.GPE.A.1

7.

FLASHCARD QUESTION

Front

What does the variable 'r' represent in the circle equation?

Back

The variable 'r' represents the radius of the circle.

Tags

CCSS.HSG.GPE.A.1

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