# How do you know if #x^2-10x-y+18=0# is a hyperbola, parabola, circle or ellipse?

##### 1 Answer

Aug 7, 2018

This is a parabola.

#### Explanation:

Given:

#x^2-10x-y+18 = 0#

Note that the only term of degree

Since the multiplier of

In fact, adding

#y = x^2-10x+18#

which clearly expresses

We can also complete the square to find:

#y = (x-5)^2-7#

allowing us to identify the vertex

graph{(x^2-10x-y+18)(x-5+0.0001y)((x-5)^2+(y+7)^2-0.01) = 0 [-6.455, 13.545, -7.88, 2.12]}