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)

Guida di studio - Domande di pratica