conics 8.1 - 8.3 (2019-20)

Which conic is given by the equation: $\left(y-8\right)^2=4\left(x+2\right)$

• Hyperbola

• Ellipse

• Circle

• Parabola

 $\left(x+10\right)^2=-16\left(y-3\right)$  
What is the equation of the directrix?

• y = 3

• x = -16

• y = -4

• y = 7

• x = -10 

 $\left(y+2\right)^2=4\left(x-9\right)$  

What are the coordinates for the focus?

•  $\left(2,-9\right)$   

•  $\left(9,-2\right)$  

•  $\left(13,-2\right)$  

•  $\left(10,-2\right)$  

•   $\left(6,-9\right)$  

 $\left(y-7\right)^2=4x+12$  

What are the coordinates for the vertex?

•  $\left(7,12\right)$   

•  $\left(4,-7\right)$  

•  $\left(-3,7\right)$  

•  $\left(7,3\right)$  

•   $\left(-12,-7\right)$  

given the characteristics for an ellipse:
foci:   $\left(7,9\right)\left(-1,9\right)$  
covertices:  $\left(3,\ 12\right)\left(3,6\right)$  
write the equation in standard form 

•  $\frac{\left(x-3\right)^2}{25}+\frac{\left(y-9\right)^2}{9}=1$  

•  $\frac{\left(x+3\right)^2}{16}+\frac{\left(y-9\right)^2}{9}=1$  

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

•  $\frac{\left(y-9\right)^2}{16}+\frac{\left(x-3\right)^2}{25}=1$  

 $\frac{\left(y+1\right)^2}{64}+\frac{\left(x-2\right)^2}{100}=1$  
where are one of the focus points located?

•  $\left(-1,10\right)$   

•  $\left(-1,-4\right)$  

•  $\left(2,-1\right)$  

•  $\left(12,-1\right)$  

•   $\left(8,-1\right)$  

 $\left(y-5\right)^2+9\left(x+4\right)^2=36$  
where are one of the covertices located?

•  $\left(-5,4\right)$   

•  $\left(-4,11\right)$  

•  $\left(-10,\ 5\right)$  

•  $\left(0,5\right)$  

•   $\left(-6,5\right)$  

given the characteristics for an ellipse:
major axis length:  14 
covertices:  $\left(6,\ 4\right)\left(12,4\right)$  
write the equation in standard form 

•  $\frac{\left(x+9\right)^2}{7}+\frac{\left(y+4\right)^2}{9}=1$  

•  $\frac{\left(y+6\right)^2}{28}+\frac{\left(x-2\right)^2}{6}=1$  

•  $\frac{\left(x+6\right)^2}{9}+\frac{\left(y-4\right)^2}{196}=1$  

•  $\frac{\left(y-4\right)^2}{49}+\frac{\left(x-9\right)^2}{9}=1$  

Which is the equation of a circle with center (2, 1) that passes through (2, 4)?

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

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

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

• $x^2+y^2=9$

What are the coordinates for the center and radius of the circle with equation: $\left(y-6\right)^2+x^2=4$

• Center (6,0)
  Radius = 4 units

• Center (6,0)
  Radius = 2 units

• Center (0,6)
  Radius = 2 units

• Center (6,0)
  Radius = 16 units