Consider the paraboloid z=x2+y2. The plane 8x−5y+z−2=0 cuts the paraboloid, its intersection being a curve. Find "the natural" parametrization of this curve. Hint: The curve which is cut lies above a circle in the xy-plane which you should parametrize as a function of the variable t so that the circle is traversed counterclockwise exactly once as t goes from 0 to 2*pi, and the parameterization starts at the point on the circle with largest x coordinate. Using that as your starting point, give the parametrization of the curve on the surface. c(t)=(x(t),y(t),z(t)), wherex(t)=y(t)=z(t)=

The parametrization of the curve on the surface is

Where

Step-by-step explanation:

From the question we are told that

The equation for the paraboloid is

The equation of the plane is

Form the equation of the plane we have that

So

=>

Using completing the square method to evaluate the quadratic equation we have

representing the above equation in parametric form

,

So from

Generally the parametrization of the curve on the surface is mathematically represented as

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i believe that john has 55 pieces of candy left.

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not only in mathematics, scientific proof also are required in the other field of science. also maths proofs are of particular structure, containing steps and logics. so proving is like doing science, it is science. that's why it is important to prove. 

an inaccurate proof leads to errors, or stating results that are not accurate.  which wil mess the probelm up you dont want this