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

May 4, 2016

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

#### Explanation:

The general standard form for a parabola with a horizontal axis of symmetry is $x = a {y}^{2} + b y + c$

(Personally I find the vertex form: $x = m {\left(y - p\right)}^{2} + q$ more useful).

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