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) isfocus (2, -2)directrix y=-8Part 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=-11Part 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) isfocus (-1,6)directrix x=-9
