The equation 4x^2 - 24xy + 11y^2 = 0 represen | vedclass

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(C) The given equation is a homogeneous equation of the second degree in $x$ and $y$ of the form $ax^2 + 2hxy + by^2 = 0$. Comparing $4x^2 - 24xy + 11

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two lines through the origin

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(C) The given equation is a homogeneous equation of the second degree in $x$ and $y$ of the form $ax^2 + 2hxy + by^2 = 0$. Comparing $4x^2 - 24xy + 11y^2 = 0$ with $ax^2 + 2hxy + by^2 = 0$,we get $a = 4$,$2h = -24$ (so $h = -12$),and $b = 11$. For a homogeneous equation of the second degree,the discriminant is $h^2 - ab = (-12)^2 - (4)(11) = 144 - 44 = 100$. Since $h^2 - ab > 0$,the equation represents two distinct real lines passing through the origin. Therefore,the correct option is $C$.

The equation $4x^2 - 24xy + 11y^2 = 0$ represents

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