Am studying for my final exam lol, this question is confusing me as well,

the equation give is f(x,y)=x^2/4 + y^2/9

(a) Sketch at least three labeled level curves of f and the gradient vector at a point on each of them.

Kay I know how to draw the level curves i set f(x,y)=z say , z constant i get an ellipse but how do I draw the gradient vectos at each point? as they say from reading from my textbook it says its orthogonal to the level curves so i just draw perpendicular lines to the points on the level curves.

(b) Find an equation to the tangent plane, at f(2,3) thats just using the the partial dervitives of fx and fy i think