What is the focus of the parabola with the equation #(x – 1)^2 + 32 = 8y#?

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Answer 1 · 2015-11-28T03:21:43

Focus #(2+1, 4) => (3,4)#

Vertex: #(1, 4)#

Directrix: #y= 1-2 => y= -1#

#(x-1)^2 +32=8y#
#(x-1)^2 = 8y-32# Subtract 32 to get isolate #(x+1)^2#

#(x-1)^2 = 8(y-4)# Factor out the greatest common factor

Focus: #(h+p, k)#

Directrix: #y= h=p#

#4p= 8 => p = 2#

Vertex: #(1, 4)#

Focus #(2+1, 4) => (3,4)#

Directrix: #y= 1-2 => y= -1#