Find the vertex, focus, and directrix for the parabolas: a) (y – 9)^2 = 8(x -2) b) y^2 – 4y = 4x – 2^2 c) (x – 6)^2 = 4(y – 2)

ossidianaZ

ossidianaZ

Answered question

2021-01-04

Find the vertex, focus, and directrix for the parabolas:
a) (y9)2=8(x2)
b) y24y=4x22
c) (x6)2=4(y2)

Answer & Explanation

funblogC

funblogC

Skilled2021-01-05Added 91 answers

a) (y9)2=8(x2)
(yk)2=4p(xh)
h=2,k=9,
4p=8
p=84=2
vertex =(h,k)=(2,9)
focus =(4,9)
directrix =x=hp=22=0
b) y24y=4x22 – transform, as a2+b2+2ab=(a+b)2, so
y24y+4=4x+4+4
(y2)2=4(x+2)
h=2,k=2
4a=4
a=1
vertex =(h,k)=(2,2)
focus =(2,3)
directx =hp=23=5
c) (x6)2=4(y2)
(xh)2=4p(yk)
h=6,k=2
4p=4
p=1
vertex =(h,k)=(6,2)
focus =(h,k+p)=(6,3)
directrix =kp=21=1

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