Graphing liner equations. please help solve (im a girl)
1 answer:
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Answer:
(x,y,z)=(ucos(v), usin(v), )
where and
Step-by-step explanation:
Equation of a cone is
Equation of a paraboloid is
I have parametrised cone here. Please note that equation for cone in the question, is actually a paraboloid.
Imagine a sphere of radius 4, centered at origin and intersecting a cone also centered at origin and height along positive z-axis, given by the equations
where
Solving for these two equations, and substituting for z in the equation of sphere, we get a circle of radius units.
The equation of intersecting circle is:
Now, according to question, parametrizing this region of circle using parameters u and v.
Consider cylindrical co-ordinates: (r,θ,z)
In cylindrical co-ordinates
(x, y, z)= (r cos(θ), r sin(θ), z)
Eliminating z, and changing (r, θ)=(u,v)
For cone: x=ucos(v)
y= usin(v)
z=
or (x,y,z)=(ucos(v), usin(v), )
where and