how do i parametrise the paraboloid given by the equation: z = x^2 + y^2? a step by step solution would be greatly apprieciated. thanks.
2007-02-11 02:05:19 · 2 answers · asked by drummanmatthew 2 in Science & Mathematics ➔ Mathematics
i knew that but i'm not sure how to use this information to parameterise it
2007-02-11 07:45:03 · update #1
you need a function from 2 dimensional space to three dimensional space such that the image is exactly the paraboloid,
here is one:
f(x,y) = (x,y, x^2+y^2)
the domain is all the pairs (x,y) and the image is exactly the paraboloid.
2007-02-12 03:58:39 · answer #1 · answered by lobis3 5 · 3⤊ 0⤋
trace x=k
z=k^2+y^2 that is parabola
trace y=k
z=x^2+k^2 that is parabola
trace z=k
k=x^2+y^2 that is circle
the surface is circular paraboloid with axis the z axis and vertex(0.0,0)
good luck
2007-02-11 10:34:59 · answer #2 · answered by Helper 6 · 2⤊ 0⤋