Classify the conic section \(x = y^2\)

a) Hyperbola

b) This is not an equation of a conic section

c) Ellipse

d) Parabola

e) Circle

Guest May 13, 2021

#1**+2 **

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 :)

NotGuest May 13, 2021