Question 1

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

Accepted Answer

$$ (x - h)^2$ + (y - k)^2$ = r^2$ $$

Question 2

Given the equation $$ x^2$ + y^2$ = 1 $$, what is the center and radius of the circle?

Accepted Answer

Center: $$(0, 0)$$, Radius: $$1$$

Question 3

Which of the following equations represents a circle with center $$(4, -7)$$ and radius $$6$$?

Accepted Answer

$$ (x - 4)^2$ + (y + 7)^2$ = 36 $$

Question 4

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

Accepted Answer

$$ x^2$ + y^2$ + Dx + Ey + F = 0 $$

Question 5

If the equation of a circle is $$ x^2$ + y^2$ - 8x + 6y + 9 = 0 $$, what are the center and radius?

Accepted Answer

Center: $$(4, -3)$$, Radius: $$4$$

Question 6

Which of the following best describes the unit circle?

Accepted Answer

A circle with center $$(0, 0)$$ and radius $$1$$

Question 7

Given the equation $$ (x - 2)^2$ + (y + 5)^2$ = 25 $$, what are the $$x-$$intercepts of the circle?

Accepted Answer

$$ (2 + \sqrt{25 - 25}, 0) $$ and $$ (2 - \sqrt{25 - 25}, 0) $$

Question 8

Which of the following equations does NOT represent a circle?

Accepted Answer

$$ x^2$ + y^2$ = -1 $$

Question 9

A circle passes through the point $$(3, 4)$$ and has center $$(1, 2). $$What is its radius?

Accepted Answer

$$ r = \sqrt{(3 - 1)^2$ + (4 - 2)^2$} $$

Question 10

If the equation $$ x^2$ + y^2$ + 6x - 8y + 9 = 0  is $$rewritten in standard form, what is the radius of the circle?

Accepted Answer

$$ 3 $$

Question 11

Which step is necessary to convert the general form $$ x^2$ + y^2$ + Dx + Ey + F = 0  to $$standard form?

Accepted Answer

Complete the square for both $$x$$ and $$y$$

Question 12

A circle has the equation $$ (x + 2)^2$ + (y - 3)^2$ = 16 . $$What is the length of its diameter?

Accepted Answer

$$ 8 $$

Question 13

If a circle's equation is $$ x^2$ + y^2$ + 2x - 4y + 1 = 0 $$, what is the center of the circle?

Accepted Answer

$$(-1, 2)$$

Question 14

Which of the following is the equation of a circle with center at the origin and radius $$r$$?

Accepted Answer

$$ x^2$ + y^2$ = r^2$ $$

Question 15

A circle has the equation $$ (x - 5)^2$ + (y + 2)^2$ = 49 . $$Which point lies on the circle?

Accepted Answer

$$(5, -9)$$

Question 16

If the equation $$ x^2$ + y^2$ + 4x + 6y + 9 = 0  is $$rewritten in standard form, what is the center of the circle?

Accepted Answer

$$(-2, -3)$$

Study Notes: Circles in the Cartesian Plane (Precalculus Chapter 1.4)

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