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 $$(3, -2)$$ and radius $$5$$?

Accepted Answer

$$(x - 3)^2$ + (y + 2)^2$ = 25$$

Question 4

If the equation of a circle is $$(x - 4)^2$ + (y + 7)^2$ = 36$$, what are the coordinates of the center and the length of the radius?

Accepted Answer

Center: $$(4, -7)$$, Radius: $$6$$

Question 5

A circle has the equation $$x^2$$ + $$y^2 - 6x + 8y = 0$. What is the center and radius of the circle?

Accepted Answer

Center: $$(3, -4)$$, Radius: $$5$$

Question 6

Which of the following is the general form of the equation of a circle?

Accepted Answer

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

Question 7

A circle is defined as the set of all points $$(x, y) in $$the plane that are a fixed distance $$r$$ from a fixed point $$(h, k). $$What are $$r$$ and $$(h, k)$$ called, respectively?

Accepted Answer

Radius and center

Question 8

What is the equation of the unit circle?

Accepted Answer

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

Question 9

Which of the following equations does NOT represent a circle in the Cartesian plane?

Accepted Answer

$$(x - 2)^2$ + (y + 3)^2$ = -4$$

Question 10

A circle has the equation $$x^2$$ + $$y^2 = 25$. What are the x$-intercepts of this circle?

Accepted Answer

$$(5, 0)$$ and $$(-5, 0)$$

Question 11

Given the general form $$x^2$$ + $$y^2 + 2x - 4y - 4 = 0$, what is the standard form of the equation of the circle?

Accepted Answer

$$(x + 1)^2$ + (y - 2)^2$ = 9$$

Question 12

A circle is centered at $$(0, 0)$$ and passes through the point $$(3, 4). $$What is its equation?

Accepted Answer

$$x^2$$ + $$y^2 = 25$

Question 13

If a circle has the equation $$(x - 2)^2$ + (y + 5)^2$ = 0$$, what does its graph look like?

Accepted Answer

A circle with radius $$0 at$$ $$(2, -5) (a $$single point)

Question 14

Which of the following real-world scenarios can be modeled by the equation of a circle?

Accepted Answer

The path traced by the tip of a clock's second hand

Question 15

A circular park has its center at $$(10, -3)$$ and a radius of $$7$$ units. Which equation models the boundary of the park?

Accepted Answer

$$(x - 10)^2$ + (y + 3)^2$ = 49$$

Question 16

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

Accepted Answer

$$5$$

Question 17

Which step is necessary to convert the general form of a circle's equation to standard form?

Accepted Answer

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

Question 18

A circle has the equation $$(x + 2)^2$ + (y - 3)^2$ = 16. $$What are the $$y-$$intercepts of this circle?

Accepted Answer

$$(0, 7)$$ and $$(0, -1)$$

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

Study Guide - Practice Questions

Study Guide - Flashcards