Add $\\left(\\frac{b}{2}\\right)^2$ to both sides

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

Question 1

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

Accepted Answer

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

Question 2

Given the equation $x^2 + 10x = 7$, what number must be added to both sides to complete the square?

Accepted Answer

$25$

Question 3

If the endpoints of a diameter of a circle are $A(-4, 3)$ and $B(2, -1)$, what is the center of the circle?

Accepted Answer

$(0, 1)$

Question 4

What is the radius of the circle whose diameter has endpoints $(-4, 3)$ and $(2, -1)$?

Accepted Answer

$rac{1}{2} \sqrt{52}$

Question 5

Which of the following is the correct process for completing the square for $x^2 + bx$?

Accepted Answer

Add $\left(\frac{b}{2}\right)^2$ to both sides

Question 6

Given the equation $(x + 2)^2 + (y - 3)^2 = 36$, what are the center and radius of the circle?

Accepted Answer

Center $(-2, 3)$, radius $6$

Question 7

If a circle has the equation $(x - 2)^2 + (y - 2)^2 = 4$, in which quadrant is its center located?

Accepted Answer

Quadrant I

Question 8

Solve $x^2 = 9$ using the square root property.

Accepted Answer

$x = \pm 3$

Question 9

What is the solution to $(x + 2)^2 = 9$?

Accepted Answer

$x = -2 \pm 3$

Question 10

A circle passes through the point $(4, 2)$ and has center at $(0, 0)$. What is its equation in standard form?

Accepted Answer

$x^2 + y^2 = 20$

Question 11

Which formula is used to find 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 12

If the equation of a circle is $x^2 + y^2 - 4x + 6y = 12$, what is the center after completing the square?

Accepted Answer

$(2, -3)$

Question 13

Which of the following is the correct way to sketch the graph of a circle given its equation $(x - h)^2 + (y - k)^2 = r^2$?

Accepted Answer

Plot the center at $(h, k)$ and draw a circle with radius $r$

Question 14

Given the equation $(x - 1)^2 + (y + 2)^2 = 25$, which point lies on the circle?

Accepted Answer

$(6, -2)$

Question 15

If the center of a circle is $(3, -2)$ and the radius is $5$, what is its equation?

Accepted Answer

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

Question 16

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 $y$ terms

Question 17

A circle has center $(0, 0)$ and passes through $(3, 4)$. What is its radius?

Accepted Answer

$5$

Question 18

If $(x - h)^2 + (y - k)^2 = r^2$ and $r = 0$, what does the graph look like?

Accepted Answer

A point at $(h, k)$

Question 19

Which of the following is a correct application of the square root property to solve $(x - 4)^2 = 9$?

Accepted Answer

$x - 4 = \pm 3$

Section 2.2: Circles – Equations, Properties, and Graphing (College Algebra Study Notes)

Study Guide - Practice Questions