Question 1

Given the unit circle equation $$x^2$$ + $$y^2 = 1$, which of the following points lies on the unit circle?

Accepted Answer

$$(\frac{1}{2}, \frac{\sqrt{3}}{2})$$

Question 2

Which of the following is the general equation of a circle centered at the origin with radius $$r$$?

Accepted Answer

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

Question 3

If a point $$(x, y)$$ satisfies $$x^2$$ + $$y^2 = 1$, what is the distance from this point to the origin?

Accepted Answer

$$1$$

Question 4

Which of the following equations represents a circle with center $$(0,0)$$ and radius $$2$$?

Accepted Answer

$$x^2$$ + $$y^2 = 4$

Question 5

If the equation of a circle is $$x^2$$ + $$y^2 = 9$, what is the length of the diameter?

Accepted Answer

$$6$$

Question 6

A circle is graphed with the equation $$x^2$$ + $$y^2 = 16$. Which of the following statements is true?

Accepted Answer

The circle passes through the point $$(0, 4).$$

Question 7

Which of the following points does NOT lie on the circle $$x^2$$ + $$y^2 = 25$?

Accepted Answer

$$(4, 4)$$

Question 8

If a circle has the equation $$x^2$$ + $$y^2$$ = $$r^2$$ and passes through the point $$(6, 8)$$, what is the value of $$r$$?

Accepted Answer

$$10$$

Question 9

Which of the following best describes the graph of $$x^2$$ + $$y^2 = 1$?

Accepted Answer

A circle centered at the origin with radius $$1$$

Question 10

If the equation $$x^2$$ + $$y^2$$ = $$r^2$$ represents a circle, what happens to the size of the circle as $$r$$ increases?

Accepted Answer

The circle gets larger.

Question 11

A circle with equation $$x^2$$ + $$y^2 = 36$ is drawn on a coordinate plane. What is the area of the circle?

Accepted Answer

$$36\pi$$

Question 12

Which of the following is the equation of a circle with center at the origin and passing through $$(0, -7)$$?

Accepted Answer

$$x^2$$ + $$y^2 = 49$

Question 13

If a circle has the equation $$x^2$$ + $$y^2 = 100$, what is the circumference of the circle?

Accepted Answer

$$20\pi$$

Question 14

Which of the following points is NOT on the unit circle $$x^2$$ + $$y^2 = 1$?

Accepted Answer

$$(1, 1)$$

Question 15

A circle is centered at the origin and has a radius of $$5. $$Which equation represents this circle?

Accepted Answer

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

Graphing Circles: Common Plane Equations

Study Guide - Practice Questions