finding direction of derivative

Question

In what directions is the derivative of ​f(x,y) = xy + y^2 at ​P(​9,1​) equal to​ zero?

Answer 1

f_x = y = 1; f_y = x + 2y = 9 + 2 = 11;

Vector v = ai + bj; a + 11b = 0 and a² + b² = 1; a = - 11b; 121b² + b² = 1; b = -1/√122; a = 11/√122

In direction of unit vector v = <-1/√122, 11/√122> directional derivative equal 0,