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: $y= 1-2 => y= -1$

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