## Question

###### Consider the paraboloid z = X? + 2y2 and the plane z=X+y+27, which intersects the paraboloid in curve C at (4,3,34) as shown in the figure to the right. Find the equation of the line tangent to C at the point (4,3,34). Proceed by completing parts (a) through (d) below:(4,3,34)a. Find vector normal to the plane at (4,3,34). Choose the correct answer below:OA (1,-1,-1)(-1,-1,1)(4,3,34)(1,1,27)b. Find vector normal to the plane tangent to the paraboloid at (4,3,34). Choose the correct answer below:

Consider the paraboloid z = X? + 2y2 and the plane z=X+y+27, which intersects the paraboloid in curve C at (4,3,34) as shown in the figure to the right. Find the equation of the line tangent to C at the point (4,3,34). Proceed by completing parts (a) through (d) below: (4,3,34) a. Find vector normal to the plane at (4,3,34). Choose the correct answer below: OA (1,-1,-1) (-1,-1,1) (4,3,34) (1,1,27) b. Find vector normal to the plane tangent to the paraboloid at (4,3,34). Choose the correct answer below: 0A: (8,12,27) (-8, 12,1) (-8, 12,27) CD; (8,12,1) The line tangent to C at (4,3,34) is orthogonal to both normal vectors found in parts (a) and (b): Use this fact to find direction vector for the tangent line. Choose the correct answer below: 0 A (0,-7,4) (-7,11,0) (11, - 7,4) 0 D. (11,0,4)