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Common Core Standard HSG-GPE.A.2 Questions

Derive the equation of a parabola given a focus and directrix.

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Grade 12 Quadratic Equations CCSS: HSG-GPE.A.2
What is the equation of a parabola with the focus at [math](2,-2)[/math] and directrix of [math]y=-6[/math]?
  1. [math](x+2)^2=32(y-4)[/math]
  2. [math]8(x-2)^2=y+4[/math]
  3. [math] (x-2)^2=4(y+4) [/math]
  4. [math](x-2)^2=8y+32[/math]
Grade 12 Quadratic Equations CCSS: HSG-GPE.A.2
What is the equation of a parabola with the focus at [math](6,-1)[/math] and directrix of [math]y=-3[/math]?
  1. [math](x-6)^2=4(y+2)[/math]
  2. [math](x-6)^2=-4(y-2)[/math]
  3. [math](x+6)^2=4(y-2)[/math]
  4. [math](x-6)^2=12(y+2)[/math]
Grade 12 Quadratic Equations CCSS: HSG-GPE.A.2
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]
Grade 12 Quadratic Equations CCSS: HSG-GPE.A.2
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]
Grade 12 Quadratic Equations CCSS: HSG-GPE.A.2
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]

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