How can you convert the general form of a circle's equation to standard form?

You can complete the square for both x and y terms to convert to standard form.

What is the significance of the constant term in the equation of a circle?

The constant term determines the size of the circle, specifically the radius.

If a circle's equation is given as $$(x - 5)^2 + (y + 6)^2 = 4$$ , what is the radius?

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

What does it mean if the radius of a circle is zero?

If the radius is zero, the circle is actually a point located at the center (h, k).

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

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

How do you graph a circle given its equation?

Identify the center (h, k) and the radius r, then plot the center and draw a circle with radius r around it.

Equation of a Circle Flashcards

Student preview

15 questions

Show all answers

1.

FLASHCARD QUESTION

Front

What is the standard equation of a circle with center (h, k) and radius r?

Back

The standard equation is $(x - h)^2 + (y - k)^2 = r^2$ .

2.

FLASHCARD QUESTION

Front

What does the 'h' in (h, k) represent in the equation of a circle?

Back

The 'h' represents the x-coordinate of the center of the circle.

3.

FLASHCARD QUESTION

Front

What does the 'k' in (h, k) represent in the equation of a circle?

Back

The 'k' represents the y-coordinate of the center of the circle.

4.

FLASHCARD QUESTION

Front

If a circle has a center at (3, -2) and a radius of 5, what is its equation?

Back

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

5.

FLASHCARD QUESTION

Front

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

Back

The radius is found by taking the square root of the constant on the right side of the equation in the form $(x - h)^2 + (y - k)^2 = r^2$ .

6.

FLASHCARD QUESTION

Front

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

Back

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

7.

FLASHCARD QUESTION

Front

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

Back

The center is (2, -3).

8.

FLASHCARD QUESTION

Front

What is the radius of the circle given by the equation $(x - 1)^2 + (y - 2)^2 = 9$ ?

Back

The radius is 3, since $r = \text{sqrt}(9) = 3$ .

9.

FLASHCARD QUESTION

Front

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

Back

The general form is $x^2 + y^2 + Dx + Ey + F = 0$ .

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