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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 $8(y – 3) = x^2$ is $1.$
1. True
2. False
3.
Identify the equation of a parabola with vertex at the origin and the directrix of $y=2$.
1. $x=-1/8y^2$
2. $y=8x^2$
3. $x=1/8y^2$
4. $y=-1/8x^2$
4.
Identify the focus of $y=4x^2.$
1. $(0,1/4)$
2. $(1/16,0)$
3. $(0,1/16)$
4. $(1/4,0)$
5.
Identify the directrix of $x=1/12y^2.$
1. $x=-3$
2. $x=3$
3. $x=-12$
4. $x=12$
6.
What is the equation of a parabola with the focus at $(3,-2)$ and directrix of $y=-10$?
1. $(x+3)^2=16(y-6)$
2. $(x-3)^2=16(y+6)$
3. $(x-3)^2=4(y+10)$
4. $(x-3)^2=-40(y+6)$
7.
What is the equation of a parabola with the focus at $(1,3)$ and a directrix of $x=-5?$
1. $(x-3)^2 = 12(y+2)$
2. $(y-3)^2 = 12(x-1)$
3. $(y+3)^2 = 3(x-2)$
4. $(y-3)^2 = 12(x+2)$
8.
What is the equation of a parabola with the focus at $(-1,18)$ and directrix of $y=12$?
1. $(x-1)^2=12(y+15)$
2. $((x+1)^2)/12=y-15$
3. $(x+1)^2+18=12y$
4. $(x+1)^2=4(y-15)$
9.
What is the equation of a parabola with the focus at $(-5,2)$ and directrix of $y=0$?
1. $(x+5)^2/4+1=y$
2. $(x+5)^2-1=4y$
3. $(x+5)^2=(y-1)$
4. $(x+5)^2=4y$
10.
What is the equation of a parabola with the focus at $(4,-5)$ and directrix $x=0?$
1. $(y-5)^2 = 8x$
2. $(y+5)^2 = 8(x - 4)$
3. $(y+5)^2 = 8x - 16$
4. $(y-5)^2 + 8 = 4x$
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