Conics - Circles and Parabolas

What is the radius of the circle:  $x^2+\left(y+3\right)^2=81$  ?

What are the center and radius for the circle:
 $\left(x+2\right)^2+\left(y-6\right)^2=9$  ?

• Center:  (-2, 6), Radius:  9

• Center:  (-2, 6), Radius:  3

• Center:  (2, -6), Radius:  3

• Center:  (2, -6), Radius:  9

What is the equation for the circle shown here?

• $\left(x-1\right)^2+\left(y+4\right)^2=16$

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

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

• $\left(x+1\right)^2+\left(y-4\right)^2=16$

What is the standard form of the equation:
 $x^2+y^2-10x+2y-10=0$  ?

•  $\left(x-5\right)^2+\left(y+1\right)^2=16$  

•  $\left(x-5\right)^2+\left(y+1\right)^2=10$  

•  $\left(x-5\right)^2+\left(y+1\right)^2=6$  

•  $\left(x-5\right)^2+\left(y+1\right)^2=36$  

What is the vertex for the parabola:
 $x=-2\left(y-3\right)^2+7$  

•  $\left(7,\ 3\right)$  

•  $\left(3,\ 7\right)$  

•  $\left(7,\ -3\right)$  

•  $\left(-3,\ 7\right)$  

What are the focus and directrix for:
 $y=-\frac{1}{12}\left(x-4\right)^2+3$  ?

• focus:  (4, 6)        directrix:  y = 0

• focus:  (4, 0)        directrix:  y = 6

• focus:  (4, 2.67)        directrix:  y = 3.33

• focus:  (-4, 0)       directrix:  y = 6

Which of the following parabolas open horizontally? Select all that apply

• 
  

   $5x+3y^2-6y+1=0$  
  

•  $y=-2\left(x+1\right)^2+2$  

•  $2x+9=5x^2-y$  

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

•  $\left(y-5\right)^2+2=-2x+8$  

What is the completed square form of the following parabolic equation:   $y=x^2+8x-3$   ?

•  $y=\left(x+4\right)^2-19$  

•  $y=\left(x+4\right)^2+13$  

•  $y=\left(x+4\right)^2-3$  

•  $y=\left(x+8\right)^2+13$  

When   $y^2+6y+8x+25=0$ is written in the standard form   $x=a\left(y-k\right)^2+h$ , what is the value of   $"a"$  ? (Write your answer as a fraction in lowest terms or as an exact decimal)

What is the equation for the parabola shown in the image?

• $y=\left(x+1\right)^2+2$

• $y=\left(x-1\right)^2+2$

• $y=\frac{1}{4}\left(x-1\right)^2+2$

• $y=\frac{1}{4}\left(x+1\right)^2+2$