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what is the graph of ax^2+by^2+cz^2=d^2 how to draw it？

what is the graph of ax^2+by^2+cz^2=d^2
how to draw it？

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Answer #1

The given equation is , ax2 + by2 + cz2 = d2 which contains three variables namely x , y , z . So this is a 3 dimensional graph we cannot plot by hand but I'm explaining shape of it and how to construct .

In 2-dimension we know that the equation ax2 + by2 = c2 represents a ellipse because this equation can be written as ,

Which is a standard equation of an ellipse .

Similarly in 3-dimension the given equation can be written as ,

Which represents the equation of paraboloid , which can be construct by rotating an two dimensional ellipse about its major axis .

The graph ( half) of the three dimensional graph ax2 + by2 + cz2 = d2 is following ,

This is somewhat look like half egg and an ellipse is just an full egg.

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