Question 1

Which of the following 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 endpoints of a diameter of a circle at $$(4, 3)$$ and $$(0, 1)$$, what is the center of the circle?

Accepted Answer

$$(2, 2)$$

Question 3

A circle has the equation $$x^2$$ + $$y^2 - 6x + 8y + 9 = 0$. What are the coordinates of its center?

Accepted Answer

$$(3, -4)$$

Question 4

Which of the following best describes the geometric definition of a circle?

Accepted Answer

A set of all points in the plane equidistant from a fixed point.

Question 5

If a circle has center $$(-3, 6)$$ and radius $$5$$, what is its equation in standard form?

Accepted Answer

$$(x + 3)^2$ + (y - 6)^2$ = 25$$

Question 6

A circle is tangent to the line $$x = 1$$ and has center at $$(4, -2). $$What is the radius of the circle?

Accepted Answer

$$3$$

Question 7

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

Accepted Answer

$$x^2$$ + $$y^2 + ax + by + c = 0$

Question 8

A clock face is a real-world example of which geometric figure?

Accepted Answer

Circle

Question 9

Given the equation $$(x - 2)^2$ + (y + 1)^2$ = 16$$, what is the radius of the circle?

Accepted Answer

$$4$$

Question 10

Which of the following steps is necessary to convert the general form $$x^2$$ + $$y^2 + 4x - 6y - 12 = 0$ to standard form?

Accepted Answer

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

Question 11

A water droplet forms a perfect circle on a surface. If the center is at $$(2, 3)$$ and a point on the edge is $$(5, 7)$$, what is the equation of the circle?

Accepted Answer

$$(x - 2)^2$ + (y - 3)^2$ = 16$$

Question 12

Which of the following statements about the geocentric model is correct?

Accepted Answer

The Earth is at the center and all motions are circular at constant speeds.

Question 13

If a circle has the equation $$(x + 1)^2$ + (y - 2)^2$ = 9$$, which point lies on the circle?

Accepted Answer

$$(2, 2)$$

Question 14

A sunflower has a circular center with a radius of $$6 cm. $$What is the area of the center?

Accepted Answer

$$36\pi cm$^2$$

Question 15

Which of the following is NOT a property of all circles?

Accepted Answer

The center must be at the origin.

Question 16

If the general form of a circle is $$x^2$$ + $$y^2 + 2x - 4y - 4 = 0$, what is the radius?

Accepted Answer

$$3$$

Question 17

A circle passes through the points $$(1, 2)$$ and has center at $$(4, -2). $$What is the radius?

Accepted Answer

$$5$$

Question 18

Which of the following real-world objects is best modeled by a circle?

Accepted Answer

A clock face

Question 19

If the equation of a circle is $$x^2$$ + $$y^2 = 49$, what is the length of the diameter?

Accepted Answer

$$14$$

Question 20

Which of the following steps is NOT part of converting the general form of a circle to standard form?

Accepted Answer

Expanding the squared terms

Circles: Equations, Graphs, and Applications in the Coordinate Plane

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