Fill color in a region

Question

I want to fill gray color to the left of the curve. Can anyone give some hints? Thanks!
 begin{tikzpicture}

begin{scope}[shift={(0,0)}]

draw [opacity=1, very thick, draw=red!50!black](2.4,4.5) {ellipse (2cm and 1cm)};

draw [very thick]  (2.6,5.5) parabola bend (3.4,4.6) (4,3.9);
  
end{scope} 
end{tikzpicture}

SebGlav · Accepted Answer

Just clip with your ellipse and fill an accurate region. Here's a very rough (but working) example:
documentclass[tikz,border=10pt]{standalone}

begin{document}

begin{tikzpicture}

draw [opacity=1, very thick, draw=red!50!black](2.4,4.5) {ellipse (2cm and 1cm)}; 
        
        draw [very thick]  (2.6,5.5) parabola bend (3.4,4.6) (4,3.9);
        
        % Here just to see the region filled        
        draw[densely dashed,orange] (2.6,5.5) parabola bend (3.4,4.6) (4,3.9) --++ (0,-1) --++ (-4,0) --++ (0,3) -|  cycle;
        
        clip (2.4,4.5) {ellipse (2cm and 1cm)};
        fill[blue,opacity=0.5] (2.6,5.5) parabola bend (3.4,4.6) (4,3.9) --++ (0,-1) --++ (-4,0) --++ (0,3) -| cycle;
          
    end{tikzpicture}

end{document}

EXPLANATION:
Below, you will see in dashed orange the region I filled.

Fill color in a region

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