Question

What is the focus of the parabola given by `-1/4(y+2)^2=(x-1)`?

Answer 1

The focus is, `(0,-2)`

Explanation:

Rewrite the equation as:

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

Please observe that this is "x" as a function or "y" which means that the parabola opens either left or right (instead of up or down).
The leading coefficient, `-1/4`, determines that which direction the parabola opens; it is negative, therefore, it opens to the left.

The equation is in vertex form so its vertex is obtained by observation, `(1, -2)`

To find the signed focal distance, f, use the following equation:

`f = 1/(4a)` where "a" is the leading coefficient.

`f = 1/(4(-1/4))`

`f = -1`

To obtain the focus, add f to the x coordinate of the vertex, `(0,-2)`