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

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

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Two lines through the origin

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(C) The given equation is a homogeneous second-degree equation of the form $ax^2 + 2hxy + by^2 = 0$.Comparing $4x^2 - 24xy + 11y^2 = 0$ with the general form,we have $a = 4$,$2h = -24$,and $b = 11$.Since the equation is homogeneous and has no constant term,it represents a pair of straight lines passing through the origin.To factorize: $4x^2 - 22xy - 2xy + 11y^2 = 0$$2x(2x - 11y) - y(2x - 11y) = 0$$(2x - y)(2x - 11y) = 0$Thus,the lines are $2x - y = 0$ and $2x - 11y = 0$,both of which pass through the origin $(0, 0)$.

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

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