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

Nov 28, 2015

Focus $\left(2 + 1 , 4\right) \implies \left(3 , 4\right)$

Vertex: $\left(1 , 4\right)$

Directrix: $y = 1 - 2 \implies y = - 1$

#### Explanation:

${\left(x - 1\right)}^{2} + 32 = 8 y$
${\left(x - 1\right)}^{2} = 8 y - 32$ Subtract 32 to get isolate ${\left(x + 1\right)}^{2}$

${\left(x - 1\right)}^{2} = 8 \left(y - 4\right)$ Factor out the greatest common factor

Focus: $\left(h + p , k\right)$

Directrix: $y = h = p$

$4 p = 8 \implies p = 2$

Vertex: $\left(1 , 4\right)$

Focus $\left(2 + 1 , 4\right) \implies \left(3 , 4\right)$

Directrix: $y = 1 - 2 \implies y = - 1$