Match the equation of a parabola to its focus and directrix.

Part 1)
y=(-x²/20)-(7x/10)+71/20> multiply by 20> 20y=-x²-14x+71
20y-71=-(x²+14x)
Complete the square. Remember to balance the equation by adding the same constants to each side
20y-71-49=-(x²+14x+49)

Rewrite as perfect squares

20y-120=-(x+7)²

20*(y-6)=-(x+7)²

-20*(y-6)=(x+7)²> (x-h)²=4p*(y-k)

vertex (h,k)> (-7,6)

4p=-20> p=-5

focus (h, k+p)> (-7,6-5)> (-7,1)

directrix y=k-p> 6+5> 11

the answer Part 1) is

focus (-7,1)

directrix y=11

Part 2) 

x=(-y²/12)-(y/3)+14/3> multiply by 12> 12x=-y²-4y+56

12x-56=-(y²+4y)

Complete the square. Remember to balance the equation by adding the same constants to each side

12x-56-4=-(y²+4y+4)

12x-60=-(y+2)²

12*(x-5)=-(y+2)²

-12*(x-5)=(y+2)²

the vertex is (5, -2)

4p=-12> p=-3

focus (h+p, k)> (5-3,-2)> (2,-2)

directrix x=h-p> x=5+3> x=8

the answer Part 2) is

focus (2,-2)

directrix x=8

Part 3)

y=(-x²/20)-(7x/10)+11/20> multiply by 20> 20y=-x²-14x+11

20y-11=-(x²+14x)

Complete the square. Remember to balance the equation by adding the same constants to each side

20y-11-49=-(x²+14x+49)

20y-60=-(x+7)²

20*(y-3)=-(x+7)²

-20*(y-3)=(x+7)²

the vertex is (-7,3)

4p=-20> p=-5

focus (h, k+p)> (-7, 3-5)> (-7, -2)

directrix y=k-p> y=3+5> y=8

the answer part 3) is

focus (-7, -2)

directrix y=8

Part 4) 

 y=(x²/12)-(x/3)-14/3> multiply by 12> 12y=x²-4x-56
12y+56=x²-4x
Complete the square. Remember to balance the equation by adding the same constants to each side
12y+56+4=(x²-4x+4)
12y+60=(x-2)²
12*(y+5)=(x-2)²

the vertex is (2,-5)
4p=12> p=3
focus (h, k+p)> (2, -5+3)> (2, -2)
directrix y=k-p> y=-5-3> y=-8

the answer Part 4) is
focus (2, -2)
directrix y=-8

Part 5) 
x=(y²/16)-(3y/4)-19/4> multiply by 16> 16x=y²-12y-76
16x+76=y²-12y
Complete the square. Remember to balance the equation by adding the same constants to each side
16x+76+36=y²-12y+36
16x+112=(y-6)²
16*(x+7)=(y-6)²

the vertex is (-7,6)
4p=16> p=4
focus (h+p, k)> (-7+4,6)> (-3,6)
directrix x=h-p> x=-7-4> x=-11

the answer Part 5) is 
focus (-3,6)
directrix x=-11

Part 6) 
 x=(y²/16)-(3y/4)-11/4> multiply by 16> 16x=y²-12y-44
16x+44=y²-12y
Complete the square. Remember to balance the equation by adding the same constants to each side
16x+44+36=y²-12y+36
16x+80=(y-6)²
16*(x+5)=(y-6)²

the vertex is (-5,6)
4p=16> p=4
focus (h+p, k)> (-5+4,6)> (-1,6)
directrix x=h-p---> x=-5-4---> x=-9

the answer part 6) is
focus (-1,6)
directrix x=-9

Either a or c

Step-by-step explanation: