For the vector field F and curve C, complete the following. a. Determine the points (if any) on the curve C at which the vector field F is tangent to C. b. Determine the points (if any) on the curve C at which the vector field F is normal to C. c. Sketch C and a few representative vectors of F on C. where C = = {(x,y): y - 3x² = -4} F= a. Where is F tangent to C? Select the correct choice below and fill in any answer boxes within your choice. OA. F is tangent to C at (Type an ordered pair. Use a comma to separate answers as needed.) OB. There are no points where F is tangent to C. OC. F is tangent to C at every point on C.

Consider the function f(x,y) = x² - 4y² - 9 and the point (-1,1). a. Find the unit vectors that give the direction of steepest ascent and steepest descent at P. b. Find a vector that points in a direction of no change in the function at P. a. What is the unit vector in the direction of steepest ascent at P? (Type exact answers, using radicals as needed.) What is the unit vector in the direction of steepest descent at P? (Type exact answers, using radicals as needed.) b. Which of the following vectors is in a direction of no change of the function at P? O A. (2,-8) OB. (8,2) OC. (-2,8) D. (8,-2)