Question

How do you find the standard form of `4y^2-8y-x+1=0`?

Answer 1

`4y^2-8y-x-1=0` is already in standard form...
but since this was asked under "Geometry of an Ellipse" the question was probably meant to be
`color(white)("XXX")4y^2-8y-x^2-1=0`

Explanation:

A general polynomial is said to be in "standard form" if every term has a degree greater than or equal to all terms that follow it.

`{:(4y^2,"degree "2),(-8y,"degree "1),(-x,"degree "1),(+1,"degree "0):}rArr "in standard form"`

However certain "special polynomials" such as those representing ellipse or hyperbola have their own "standard forms".

If the given equation was meant to have `(x^2)` instead of simply `x` then the equation would be a hyperbola (and not an ellipse) so I'm not certain what was intended.