Question: Better visibility of some plot

hi, do you know how can we smooth this ellipse and make it more clear?

thickness, grid, numpoints don't help

restart;
with(plots);
f := (x, y) -> x^2 + y^2 - 12*x + 16*y;
display(plot3d(f(x, y), x = -9 .. 9, y = -9 .. 9), pointplot3d([[6, -8, f(6, -8)]], color = red, symbol = solidcircle, symbolsize = 18), view = [-4.2 .. 8.2, -8.2 .. 4.2, -100 .. 100], plot3d([cos(t), sin(t), 1 - 12*cos(t) + 15*sin(t)], t = 0 .. 2*Pi, orientation = [-15, 68, 5]));
 

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