Question

Find the focus of the parabola whose equation is y=1/8 x^2

Answer 1

Answer:

The focus is: $(0,2)$

Step-by-step explanation:

Given

$y = \frac{1}{8}x^2$

Required

Determine the focus

The focus of a parabola

$(x- h)^2 = 4p(y - k)$

is:

$(h,k+p)$

So, we have:

$y = \frac{1}{8}x^2$

Cross multiply

$8y = x^2$

Rewrite as:

$x^2 = 8y$

Rewrite as:

$(x - 0)^2 = 8(y - 0)$

Express 8 as 4 * 2

$(x - 0)^2 = 4 * 2(y - 0)$

By comparison with: $(x- h)^2 = 4p(y - k)$

$h = 0$    $p =2$     $k = 0$

So, the focus $(h,k+p)$ is:

$(h,k+p) = (0,0+2)$

$(h,k+p) = (0,2)$