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]}