Part I: Activity (Circle)(Recorded and Graded)

Which of the following equations represent the standard form of the circle ?

• $\left(x+a\right)^2+\left(y+b\right)^2=r^2$

• $\left(x-a\right)^2+\left(y-b\right)^2=r^2$

• $\left(x-a\right)^2+\left(y+b\right)^2=r^2$

• $\left(x+a\right)^2+\left(y-b\right)^2=r^2$

Which of the following statements is TRUE?

• The graph of the circle is empty if $r^2>0$ .

• The graph is a circle when $r^2<0$ .

• The graph consists of a single point when $r^2=0$

• None of the above

What is the center of the circle  $x^2+y^2=4$  ?

• (0,-1)

• (0,1)

• (0,0)

• (1,0)

What is the center of the circle  $\left(y-3\right)^2+\left(x+2\right)^2=4$ ? 

• (3,-2)

• (-3,2)

• (2,-3)

• (-2,3)

Given a circle of  $\left(y-3\right)^2+\left(x+2\right)^2=4$  , what is its radius?

• 1

• 2

• 3

• 4

Which of the following equation represent the standard form of the circle  $x^2+y^2-4x+6y-12=0$ ?

•  $\left(x-2\right)^2+\left(y-3\right)^2=1$  

•  $\left(x-2\right)^2+\left(y+3\right)^2=1$  

•  $\left(x+2\right)^2+\left(y+3\right)^2=1$  

•  $\left(x+2\right)^2+\left(y-3\right)^2=1$  

Given the equation  $x^2+y^2-3x+8y+12=0$  , what is the standard form of the given circle?

•  $\left(x-\frac{3}{2}\right)^2+\left(y+4\right)^2=\frac{25}{4}$  

•  $\left(x-\frac{3}{2}\right)^2+\left(y-4\right)^2=\frac{25}{4}$  

•  $\left(x+\frac{3}{2}\right)^2+\left(y-4\right)^2=\frac{25}{4}$  

•  $\left(x+\frac{3}{2}\right)^2+\left(y+4\right)^2=\frac{25}{4}$  

Which of the following is the general form of the equation  $\left(x+4\right)^2+\left(y-6\right)^2=16$  ?

•  $x^2+y^2-12x+8y+36$  

•  $x^2+y^2+8x-12y-36$  

•  $x^2+y^2+12x-8y+36$  

•  $x^2+y^2+8x-12y+36$  

Which of the following is the general form of the equation  $\left(x-1\right)^2+y^2=7$  ?

•  $x^2+y^2+2x+6=0$  

•  $x^2+y^2-2x-6=0$  

•  $x^2+y^2-2x+6=0$  

•  $x^2+y^2+2x-6=0$  

Which of the following equation is the standard form of the equation  $4x^2+4y^2-4y=7$  ?

•  $x^2+\left(y+\frac{1}{4}\right)^2=\frac{8}{4}$  

•  $x^2+\left(y+\frac{1}{2}\right)^2=2$  

•  $x^2+\left(y-\frac{1}{2}\right)^2=2$  

•  $x^2+\left(y-\frac{1}{4}\right)^2=\frac{8}{4}$