Question

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

Answer 1

The focus is:
`(0,2)`

Explanation:

Given

`y = (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 = (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)`