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Parabolas - Focus and Directrix (Grades 11-12)

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Parabolas - Focus and Directrix

1. 
TRUE or FALSE. A Parabola has two focus points or foci.
  1. True
  2. False
2. 
The distance of the directrix from the vertex of the parabola [math]8(y – 3) = x^2[/math] is [math]1.[/math]
  1. True
  2. False
3. 
Identify the equation of a parabola with vertex at the origin and the directrix of [math]y=2[/math].
  1. [math]x=-1/8y^2[/math]
  2. [math]y=8x^2[/math]
  3. [math]x=1/8y^2[/math]
  4. [math]y=-1/8x^2[/math]
4. 
Identify the focus of [math]y=4x^2.[/math]
  1. [math](0,1/4)[/math]
  2. [math](1/16,0)[/math]
  3. [math](0,1/16)[/math]
  4. [math](1/4,0)[/math]
5. 
Identify the directrix of [math]x=1/12y^2.[/math]
  1. [math]x=-3[/math]
  2. [math]x=3[/math]
  3. [math]x=-12[/math]
  4. [math]x=12[/math]
6. 
What is the equation of a parabola with the focus at [math](3,-2)[/math] and directrix of [math]y=-10[/math]?
  1. [math](x+3)^2=16(y-6)[/math]
  2. [math](x-3)^2=16(y+6)[/math]
  3. [math](x-3)^2=4(y+10)[/math]
  4. [math](x-3)^2=-40(y+6)[/math]
7. 
What is the equation of a parabola with the focus at [math](1,3)[/math] and a directrix of [math]x=-5?[/math]
  1. [math](x-3)^2 = 12(y+2)[/math]
  2. [math](y-3)^2 = 12(x-1)[/math]
  3. [math](y+3)^2 = 3(x-2)[/math]
  4. [math](y-3)^2 = 12(x+2)[/math]
8. 
What is the equation of a parabola with the focus at [math](-1,18)[/math] and directrix of [math]y=12[/math]?
  1. [math](x-1)^2=12(y+15)[/math]
  2. [math]((x+1)^2)/12=y-15[/math]
  3. [math](x+1)^2+18=12y[/math]
  4. [math](x+1)^2=4(y-15)[/math]
9. 
What is the equation of a parabola with the focus at [math](-5,2)[/math] and directrix of [math]y=0[/math]?
  1. [math](x+5)^2/4+1=y[/math]
  2. [math](x+5)^2-1=4y[/math]
  3. [math](x+5)^2=(y-1)[/math]
  4. [math](x+5)^2=4y[/math]
10. 
What is the equation of a parabola with the focus at [math](4,-5)[/math] and directrix [math]x=0?[/math]
  1. [math](y-5)^2 = 8x[/math]
  2. [math](y+5)^2 = 8(x - 4)[/math]
  3. [math](y+5)^2 = 8x - 16[/math]
  4. [math](y-5)^2 + 8 = 4x[/math]
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