Question

The focus point of the parabola?

Answer 1

The focus point of the parabola is (2,-2).

Answer 2

`(2,- 1)`

Step-by-step explanation

The given parabola is

`y = (1)/(4) {x}^(2) - x - 1`

We need to write this parabola in the vertex form by completing the square,

`y = (1)/(4) ( {x}^(2) - 4x) - 1`

`y = (1)/(4) ( {x}^(2) - 4x + 4) - (1)/(4) * 4 - 1`

`y = (1)/(4) (x - 2 )^(2) - 2`

`{(x - 2)}^(2) = 4(y + 2)`

The vertex is

(2,-2)

The focal length is

`p = 1`

The focus is

`(2,-2 + 1)`

`(2,- 1)`