# Let A be a symmetric 2 \times 2 matrix and let k be a scalar. Prove that the graph of the quadratic equation x^T Ax=k is ,an ellipse, circle

Let A be a symmetric $$\displaystyle{2}\times{2}$$ matrix and let k be a scalar. Prove that the graph of the quadratic equation $$\displaystyle{x}^{{T}}$$ Ax=k is ,an ellipse, circle, or imaginary conic if $$\displaystyle{k}\ne{q}{0}$$ and det A > 0

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