Math 3 Circles Review for Test

 $(x+3)^2\ +\ \ (y\ –\ 5)^2=16$  Has what center and radius?

• Center at (3,-5) and radius of 16

• Center at (-3,5) and radius of 16

• Center at (3,-5) and radius of 4

• Center at (-3,5) and radius of 4

What value of c makes this a perfect square trinomial?

 $x^2-9x+c$  

•  $c=3$  

•  $c=9$  

•  $c=20.25$  

•  $c=81$  

Determine what numbers must go into the blanks shown in order to complete the square to write this equation in standard form for a circle.

 $\left(x^2+6x+_-\right)+\left(y^2-18y+_-\right)=-6+_-+_-$  

•  $12,\ 36,\ 12,\ 36$  

•  $9,\ 81,\ -9,\ -81$  

•  $12,\ -36,\ -12,\ 36$  

•  $9,\ 81,\ 9,\ 81$  

College Prep Only:
 $x^2+y^2-2x+4y+4=0$  
Rewrite the equation so that it is in standard form for a circle.  That is, complete the square.

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

•  $\left(x-1\right)^2+\left(y+2\right)^2=5$  

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

•  $\left(x+1\right)^2+\left(y-2\right)^2=5$  

Honors Only:
 $3x^2+3y^2-6x+12y+12=0$  
Rewrite the equation so that it is in standard form for a circle.  That is, complete the square.

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

•  $\left(x-1\right)^2+\left(y+2\right)^2=5$  

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

•  $\left(x+1\right)^2+\left(y-2\right)^2=5$  

What is center of this circle?

 $x^2+y^2-6x+20y=m$  

•  $\left(-6,20\right)$  

•  $\left(-3,10\right)$  

•  $\left(3,-10\right)$  

•  $\left(6,-20\right)$  

Which of the following points lies on the circle with the equation

 $\left(x+4\right)^2+\left(y-1\right)^2=25$  ?

•  $\left(-4,1\right)$  

•  $\left(0,4\right)$  

•  $\left(1,6\right)$  

•  $\left(4,3\right)$  

Write the equation of a circle with ends of a diameter at (4,-4) and (8,0).

• $\left(x-4\right)^2+\left(y+4\right)^2=64$

• $\left(x-6\right)^2+\left(y+2\right)^2=8$

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

• $\left(x-6\right)^2+\left(y+2\right)^2=\sqrt{8}$

By definition, a secant is

• a line that intersects a circle at exactly one point.

• a segment that has both endpoints on the circle.

• a line that intersects a circle at exactly two points.

• a segment that passes through the center of the circle.

 $\angle TAC\$  is what type of angle?

• inscribed angle

• circumscribed angle

• central angle

• right angle