When does the equation ax^2 + 2hxy + by^2 + 2 | vedclass

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(B) The general second-degree equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represents a conic section.Here,$\Delta$ is the determinant of the mat

Vedclass · Accepted Answer

$\Delta 
eq 0, h^2 < ab$

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(B) The general second-degree equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represents a conic section.Here,$\Delta$ is the determinant of the matrix $\begin{bmatrix} a & h & g \ h & b & f \ g & f & c \end{bmatrix}$.For the equation to represent an ellipse,the following conditions must be satisfied:$1$. $\Delta 
eq 0$ (non-degenerate conic).$2$. $h^2 - ab < 0$,which implies $h^2 < ab$.

When does the equation $ax^2 + 2hxy + by^2 + 2gx + 2fy + c = 0$ represent an ellipse?

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