How do you find the vertex, focus and directrix of #( y - 2)^2 = 4(x - 1)#?

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Answer 1 · 2018-07-09T06:45:35

Please see the explanation below.

The standard equation of the parabola is

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

Comparing our equation

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

To the standard equation

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

The focus is #F=(a+p/2,b)=(1+2/2,2)=(2, 2)#

And the directrix is

#x=a-p/2#

#x=1-2/2=0#

graph{((y-2)^2-4(x-1))=0 [-13.11, 15.36, -4.88, 9.36]}