Determine the equation of a plane tangent to the surface defined by f(x,y)=x2 + y2 at...

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Determine the equation of a plane tangent to the surface defined by f(x,y)=√x2 + y2 at the point (3,4,5). (a) Find a parameterization for the x - 3 trace of f. What is a direction vector for the line tangent to this trace at the point (3, 4, 5)? (b) Find a parameterization for the y = 4 trace of f. What is a direction vector for the line tangent to this trace at the point (3, 4, 5)? (c) The direction vectors in parts (a) and (b) form a plane containing the point (3,4,5). What is a normal vector for this plane? (d) Use your work in parts (a), (b), and (c) to determine an equation for the tangent plane. Determine the equation of a plane tangent to the surface defined by f(x,y)=√x2 + y2 at the point (3,4,5). (a) Find a parameterization for the x - 3 trace of f. What is a direction vector for the line tangent to this trace at the point (3, 4, 5)? (b) Find a parameterization for the y = 4 trace of f. What is a direction vector for the line tangent to this trace at the point (3, 4, 5)? (c) The direction vectors in parts (a) and (b) form a plane containing the point (3,4,5). What is a normal vector for this plane? (d) Use your work in parts (a), (b), and (c) to determine an equation for the tangent plane.