How do you find the vertex, focus, and directrix of the parabola #y^2-4y-4x=0#?

Question

53748 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-01-04T12:56:41

The vertex is V #=(-1,2)#
The focus is F #=(0,2)#
The directrix is #x=-2#

Let's rearrange the equation and complete the squares

#y^2-4y=4x#

#y^2-4y+4=4x+4#

#(y-2)^2=4(x+1)#

Comparing this equation to

#(y-b)^2=2p(x-a)#

#p=2#

The vertex is V #=(a,b)=(-1,2)#

The focus is F #=(a+p/2,b)=(0,2)#

The directrix is #x=a-p/2#

#x=-1-1=-2#

graph{(y^2-4y-4x)(y-100x-200)=0 [-10, 10, -5, 5]}