Module 12 Review (Conics)

 $\left(x-h\right)^2+\left(y-k\right)^2=r^2$  is the equation of a(n)...

• Circle

• Ellipse

• Parabola

• hyperbola

 $\frac{\left(x-h\right)^2}{a^2}+\frac{\left(y-k\right)^2}{b^2}=1$  is the equation of a(n)...

• Ellipse

• Circle

• Parabola

• Hyperbola

Where is the center of  $\left(x+3\right)^2+\left(y-2\right)^2=16$  ?

•  $\left(-3,\ 2\right)$  

•  $\left(3,2\right)$  

•  $\left(-3,-2\right)$  

•  $\left(3,-2\right)$  

What is the radius of $\left(x+2\right)^{2\ }+\left(y+4\right)^{2\ }=9$  ?

• 3

• 2

• 4

• 9

Where is the center of $\frac{\left(x+4\right)^2}{25}+\frac{\left(y-7\right)^2}{36}=1$  ?

•  $\left(-4,\ 7\right)$  

•  $\left(4,\ -7\right)$  

•  $\left(5,\ 6\right)$  

•  $\left(-5,\ -6\right)$  

What is the length and orientation of the major axis of $\frac{\left(x-6\right)^2}{25}+\frac{\left(y+1\right)^2}{49}=1$  ?

• 14 vertical

• 7 vertical 

• 7 horizontal

• 10 horizontal

What value completes the square for $x^2+14x+$  ______ ?

• 49

• 7

• 14

• 196

 $x^2-12x+36$  is a perfect square trinomial. How does it factor? 

•  $\left(x-6\right)^2$  

•  $\left(x+12\right)\left(x-3\right)$  

•  $\left(x-12\right)^2$  

•  $\left(x-4\right)\left(x-9\right)$  

Use completing the square to rewrite the equation in standard form: $x^2+y^2+4x-10y-52=0$  (work it out on paper!)

•  $\left(x+2\right)^2+\left(y-5\right)^2=81$  

•  $\left(x+2\right)^2+\left(y+5\right)^2=29$  

•  $\frac{\left(x+2\right)^2}{4}+\frac{\left(y+5\right)^2}{25}=52$  

•  $\left(x+4\right)^2+\left(y-10\right)^2=52$  

Use completing the square to rewrite the equation in standard form: $4x^2+y^2-8x+2y-31=0$  (work it out on paper!)

•  $\frac{\left(x-1\right)^2}{9}+\frac{\left(y+1\right)^2}{36}=1$  

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

•  $\frac{\left(x-1\right)^2}{4}+\frac{\left(y-1\right)^2}{9}=1$  

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