What Is The Formula Of \

     
I have plotted this equation $x^2=y^2-z^2$ using Wolfram|Alpha và I got this graph:

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I have made these changes to lớn the equation:

First equation solution:

$y=-sqrty^2-x^2$

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Second equation solution:

$y=sqrty^2-x^2$

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I want lớn make this by hand. How vị I can bởi it? Which coordinate system I need to lớn use to graph it?


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Write it as $x^2 + z^2 = y^2$. Cảnh báo that y is the hypotenuse of a triangle with length x và height z. So, this forms a circular cone opening as you increase in y or decrease in y.

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This figure is the (double) cone of equation $x^2=y^2-z^2$.

The gray plane is the plane $(x,y)$.

You can see that it is a cone noting that for any $y=a$ the projection of the surface on the plane $(x,z)$ is a circumference of radius $a$ with equation $z^2+x^2=a^2$.

Note that $z=sqrty^2-x^2$ is the semi-cone with $z>0$, i.e. Above the plane $(x,y)$ và $z=-sqrty^2-x^2$ is the semi-cone below this plane.

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y^2 = x^2 + z^2 has the khung of an equation for a circle. So, you are stacking, in the y direction, circles of increasing radius, one on đứng top of the other.


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