So I was searching up conic sections and google tells me all of them that are not degenerate cases.
Parabola, hyperbola, ellipse, circle, and triangle WHAT?!! So a dug around wikipedia looking for answers and apparently conic sections are not sections of cones as solid figures but of conical surfaces which have no faces and exstend out forever (a doubled mirror style conical surface is what most people refer to when they speak of conic sections). Google was answering my question correctly from what I techniqually asked. My point then is their must be some infinetly exstened triangular anoluge as the new fifth conical surface cross-section.
I came up with the following equation!
\(\frac{x^2}{a}+\frac{y^2}{b}=cx^2\) where b & c are on the interval \((0, ∞)\) and a is on the interval that is the union of \((-∞, 0)\) and \((1, ∞)\)
My question is if this counts as a conic section because I see two very large triangles :D Similar to a hyperbola the plane would cut through both parts of the conical surface but would also cut right through the apex? I am having trouble picturing if this makes sense or not
I also have accompaning hyperbolas that when superimposed form a nice graph, it is like the triangle graph acts as the oblique asymptotes of each hyperbola!
\(4x^2-y^2=1\) and \(4x^2-y^2=-1\) if you use the equation \(\frac{x^2}{5}+\frac{y^2}{5}=x^2\)
