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

 May 13, 2021

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 :)

 May 13, 2021
edited by NotGuest  May 13, 2021

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