If the normals to the ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ at the points $\left(X_1,y_1\right),\left(x_2,y_2\right)\text{and}\left(x_3,y_3\right)$ are concurrent, prove that $\left|\begin{array}{ccc}{x}_1& y_1& x_1{y}_1\\ x_2& y_2& x_2{y}_2\\ x_3& y_3& x_3{y}_3\end{array}\right|=0$.

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