Question

How do you identify the following equation `x = (y + 4)^2 - 2` as a circle, parabola, ellipse or hyperbola?

Answer 1

`x=(y+4)^2-2` is a parabola with a horizontal axis of symmetry.

Explanation:

Consider the related equation:
`color(white)("XXX")y=(x+4)^2-2`
which is the standard form for a parabola with a vertical axis of symmetry.

The given equation simply has exchanged the `x` and `y` variables, effectively exchanging the x and y axis.