What is the radius of a circle given the equation $$(x+3)^2 + (y-4)^2 = 16$$ ?

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

Convert the general form of a circle's equation $$x^2 + y^2 + 6x - 8y + 9 = 0$$ to standard form.

The standard form is $$(x+3)^2 + (y-4)^2 = 16$$ .

What is the radius of a circle with the equation $$x^2 + y^2 = 25$$ ?

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

How do you determine the radius from the equation of a circle in standard form?

The radius is found by taking the square root of the number on the right side of the equation, $$r = \text{sqrt}(r^2)$$ .

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

The general form is $$Ax^2 + Ay^2 + Bx + Cy + D = 0$$ , where A, B, C, and D are constants.

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

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

What is the radius of the circle represented by the equation $$(x-5)^2 + (y+2)^2 = 64$$ ?

The radius is 8, since $$r^2 = 64$$ , thus $$r = \text{sqrt}(64) = 8$$ .

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

Complete the square for both x and y terms to rewrite the equation in standard form.

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

The radius determines the size of the circle; a larger radius means a larger circle.

Equation of 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

2.

FLASHCARD QUESTION

Front

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

Back

3.

FLASHCARD QUESTION

Front

Back

4.

FLASHCARD QUESTION

Front

Back

5.

FLASHCARD QUESTION

Front

Back

6.

FLASHCARD QUESTION

Front

Back

This represents a circle with center (1, -2) and radius 3.

7.

FLASHCARD QUESTION

Front

If a circle has a center at (0,0) and a radius of 7, what is its equation?

Back

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