The equation x^2 + ky^2 + 4xy = 0 represents | vedclass

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(C) The general equation of a pair of straight lines passing through the origin is given by $ax^2 + 2hxy + by^2 = 0$.For this equation to represent a

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$4$

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(C) The general equation of a pair of straight lines passing through the origin is given by $ax^2 + 2hxy + by^2 = 0$.For this equation to represent a pair of coincident lines,the condition $h^2 - ab = 0$ must be satisfied.Comparing the given equation $x^2 + 4xy + ky^2 = 0$ with the general form,we have $a = 1$,$2h = 4$ (so $h = 2$),and $b = k$.Substituting these values into the condition $h^2 - ab = 0$:$(2)^2 - (1)(k) = 0$$4 - k = 0$$k = 4$.

The equation $x^2 + ky^2 + 4xy = 0$ represents two coincident lines,if $k =$

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