8.1 - 8.3 test

find the focus point for the equation:
 $x^2=4\left(y-5\right)$  

•  $\left(0,6\right)$  

•  $\left(4,5\right)$  

•  $\left(4,0\right)$  

•  $\left(5,1\right)$  

the equation below best represents:
 $3x^2+12x+4y-6=0$  

• circle

• hyperbola

• parabola

• ellipse

given: 
focus:  $\left(11,-4\right)$  directrix:  $x=5$  

write the equation of the parabola in standard form:

•  $\left(y-4\right)^2=8\left(x-11\right)$  

•  $\left(x-8\right)^2=16\left(y-4\right)$  

•  $\left(y+4\right)^2=12\left(x-8\right)$  

•  $\left(x+5\right)^2=4\left(y+4\right)$  

if the focus is located at:  $\left(-1,-5\right)$  which function best models the given parabola.

•  $\left(y+5\right)^2=-8\left(x-1\right)$  

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

•  $\left(y-5\right)^2=-12\left(x-1\right)$  

•  $\left(x+5\right)^2=4\left(y+1\right)$  

Identify the shape and center of the given equation:  $4x^2+y^2-32x+16y=-124$  

• hyperbola with center (16, -8)

• ellipse with center (16, -8)

• ellipse with center (4, -8)

• hyperbola with center (4, -8)

Write an equation for the ellipse with foci (-2, 1) and (-2, 5) and major axis endpoints (-2, -1) and (-2, 7).

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Find the foci of the given ellipse:  $4\left(y-2\right)^2+\left(x+3\right)^2=16$  

•  $\left(-3,\ 2\pm2\sqrt{3}\right)$  

•  $\left(-3\pm2\sqrt{3},\ 2\right)$  

•  $\left(-3\pm12,\ 2\right)$  

•  $\left(2,\ -3\pm12\right)$  

Choose the correct graph for the equation above.

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Which of these equations represent a circle?
A.  $x^2+2y^2-5=0$  
B.  $2x^2-5=y^2$  
C.  $2x^2-2y^2-5=0$  
D.  $2x^2+2y^2-5=0$  

• A

• B

• C

• D

Let P be any point on the curve, and F₁ and F₂ represent the coordinates of the foci, what shape is represented by this definition: PF₁ + PF₂ = 2a

• circle

• parabola

• ellipse

• hyperbola