Question

What kind of conic is `4x^2-9x+y-5=0`?

Answer 1

A parabola.

Explanation:

Please read the reference regarding Conic Sections .

The given equation:

`4x^2-9x+y-5=0" [1]"`

Matches the equation in the reference:

`Ax^2 + Bxy + Cy^2 + Dx + Ey + F = 0" [2]"`

When `A = 4, B = 0, C = 0, D = -9, E = 1 and F = -5`

The section entitled "Discriminant" tells us how do identify what type of conic section this is by evaluating the expression:

`B^2 -4(A)(C)`

Substituting in the values for A, B and C:

`0^2 - 4(4)(0) = 0`

This tells us that the conic section is a parabola.

There are other ways to do this identification but this is the most general method that I have found; that is why I wanted to share it with you.