Question #200497

Identify and trace the conicoid y2 +z2 = x. Describe its sections by the planes x = 0, y = 0 and z = 0


1
Expert's answer
2021-06-14T17:56:57-0400

y2+z2=xy^2+z^2=x


Now we can see that our surface is spherical ellipsoid.


Denominators are equal. It means that our ellipsoid is not a ellipsoid of revolution.


Let y=0y=0, then z2=xz^2 = x

And let z=0z=0, then y2=xy^2=x

z2=xz^2 = x and y2=xy^2=x principal parabolas.



Let's look on sections.


    \implies y=0y=0

    \implies z2=xz^2 = x ...................Parabola with its axis along x - axis.



    \implies  z=0z=0

    \impliesy2=xy^2 = x .................Parabola with its axis along x - axis.




    \implies x=0x=0 

    \impliesy2+z2=0y^2 + z^2 = 0 


y2+z2=xy^2+z^2=x


Now we can see that our surface is spherical ellipsoid.


Denominators are equal. It means that our ellipsoid is not a ellipsoid of revolution.


Let y=0y=0, then z2=xz^2 = x

And let z=0z=0, then y2=xy^2=x

z2=xz^2 = x and y2=xy^2=x principal parabolas.



Let's look on sections.


    \implies y=0y=0

    \implies z2=xz^2 = x ...................Parabola with its axis along x - axis.



    \implies  z=0z=0

    \impliesy2=xy^2 = x .................Parabola with its axis along x - axis.




    \implies x=0x=0 

    \impliesy2+z2=0y^2 + z^2 = 0 ...........It represents x- axis.


Thecurve is shown below:






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