Find parametric equations for the line tangent to the curve of intersection of the surfaces at the given point surfaces: x^2 + y^2 = 4, y=1

Point: (1/2, 1, 1/2)

The  parametric equation is  

Step-by-step explanation:

From the  question we are told that

   The  equation given are  

           and  y =  1  

Thus

  Let  

  And  

Now  we will differentiate f(x, y , z ) and  g(x,y,z) to obtain value  of f(x,y,z )  and    g(x,y,z) where the line passed through

 So

At  Point: (1/2, 1, 1/2)

converting to coordinate form

And

At  Point: (1/2, 1, 1/2)

converting to coordinate form

At point of intersection we have that

=>

=>  

Thus the parametric equation is  

=>    

=>    

and