Classify the conic section \(x = y^2\)
b) This is not an equation of a conic section
It is a parabola with the vertex at (0,0).
Here is a picture of the graph x = y^2
A parabola is a "symmetrical open plane curve formed by the intersection of a cone with a plane parrallel to its side." As you can see, this is exactly what that looks like.
A hyperbola is the same but with two cones, although on the graph there is not another parabola extending the other way, therefore it is not a hyperbola.
An ellipse is a fancy word for an oval, and as you can see, the lines going outward will never even intersect, therefore it is not an ellipse.
A circle is just a circle, and it is pretty obvious that this is not one.
And, because it is a parabola, it is an equation of a conic section.
Therefore, this is a d) Parabola
Hope this helps :)