a = 0;  b = 0;

q = 1; r = 2; s = 2;

u = -2; v = 2;

w = -2; z = 2;

f[x_, y_] :=  x^2  -  y^2

fx[x_, y_] := Evaluate[D[f[x, y], x]]

fy[x_, y_] := Evaluate[D[f[x, y], y]]

TangentPlane[x_, y_] := 
      f[a, b] + {fx[a, b], fy[a, b]} . {x - a, y - b}

NormalLine[t_] := {a, b, f[a, b]} + 
        t {fx[a, b], fy[a, b], -1}

Plot3D[f[x, y], {x, -2, 2}, {y, -2, 2},  
        ViewPoint -> {q, r, s}, Mesh -> False, 
        AspectRatio -> 1, 
        DisplayFunction -> Identity];
Plot3D[TangentPlane[x, y], {x, u, v}, {y, w, z}, 
        ViewPoint -> {q, r, s}, AspectRatio -> 1, 
        DisplayFunction -> Identity];
ParametricPlot3D[Evaluate[NormalLine[t]], {t, -2, 2}, 
        ViewPoint -> {q, r, s}, AspectRatio -> 1, 
        DisplayFunction -> Identity];
Show[%, %%, %%%, 
        DisplayFunction -> $DisplayFunction];