Question

How do you find the standard form of `2y^2-x-8y+5=0` and what kind of a conic is it?

Answer 1

`2y^2-x-8y+5=0`
is a parabola with a horizontal axis of symmetry
and a standard form: `x=2y^2-8y+5`

Explanation:

The general standard form for a parabola with a horizontal axis of symmetry is `x=ay^2+by+c`

(Personally I find the vertex form: `x=m(y-p)^2+q` more useful).

graph{x=2y^2-8y+5 [-6.874, 7.17, -2.05, 4.97]}