Question 1

Which of the following is the correct equation for a circle with center $$(-3, 2)$$ and radius $$5$$?

Accepted Answer

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

Question 2

Given the points $$A(2, 5)$$ and $$B(8, 11)$$, what is the midpoint of the line segment $$AB$$?

Accepted Answer

$$(5, 8)$$

Question 3

What is the slope of the line passing through the points $$(4, -2)$$ and $$(7, 10)$$?

Accepted Answer

$$rac{12}{3}$$

Question 4

Which of the following is the equation of the line in point-slope form that passes through $$(1, -3)$$ with slope $$m = 2$$?

Accepted Answer

$$y + 3 = 2(x - 1)$$

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

Find the equation of the line parallel to $$y = -rac{1}{2}x + 7$$ passing through $$(4, -1) in $$slope-intercept form.

Accepted Answer

$$y = -rac{1}{2}x + 1$$

Question 7

Which of the following is the correct distance between the points $$(1, 2)$$ and $$(4, 6)$$?

Accepted Answer

$$5$$

Question 8

A line passes through $$(2, 3)$$ and is perpendicular to the line $$y = 2x - 5. $$What is the equation of the line in point-slope form?

Accepted Answer

$$y - 3 = -\frac{1}{2}(x - 2)$$

Question 9

Given the equation $$y = 3x - 4$$, what is the $$y-$$intercept?

Accepted Answer

$$-4$$

Question 10

Which of the following is the equation of a horizontal line passing through $$(0, 6)$$?

Accepted Answer

$$y = 6$$

Question 11

If $$f(x) = 2x^2$ - 3x + 1$$, what is $$f(4)$$?

Accepted Answer

$$21$$

Question 12

Find the equation of the circle with center $$(5, -2)$$ and passing through the point $$(8, 2).$$

Accepted Answer

$$(x - 5)^2$ + (y + 2)^2$ = 25$$

Question 13

Which of the following is the correct formula for the distance between two points $$(x_1$, y_1$)$$ and $$(x_2$, y_2$)$$?

Accepted Answer

$$\sqrt{(x_2$ - x_1$)^2$$ + ($$y_2$$ - $$y_1)^2$}$$

Question 14

A line has the equation $$3x - 4y = 12. $$What is the slope of this line?

Accepted Answer

$$\frac{3}{4}$$

Question 15

Which of the following is the equation of a circle with center $$(0, 0)$$ and radius $$7$$?

Accepted Answer

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

Question 16

If a line passes through $$(1, 2)$$ and $$(5, 10)$$, what is its equation in slope-intercept form?

Accepted Answer

$$y = 2x - 2$$

Question 17

Which of the following is the correct equation for a vertical line passing through $$(4, -3)$$?

Accepted Answer

$$x = 4$$

Question 18

Given the equation $$x^2$$ + $$y^2 + 2x - 4y = 20$, what is the center and radius of the circle?

Accepted Answer

Center $$(-1, 2)$$, Radius $$5$$

Question 19

A line is perpendicular to $$y = -3x + 2$$ and passes through $$(0, 1). $$What is its equation in slope-intercept form?

Accepted Answer

$$y = \frac{1}{3}x + 1$$

Question 20

If $$f(x) = x^2$ - 4x + 7$$, what is the $$x-$$coordinate of the vertex of the parabola?

Accepted Answer

$$2$$

Lines and Circles: Equations, Graphs, and Applications

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