The lines represented by the equation 9x^2 + | vedclass

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(A) The given equation is $9x^2 + 24xy + 16y^2 + 21x + 28y + 6 = 0$.This can be written as $(3x + 4y)^2 + 7(3x + 4y) + 6 = 0$.Let $u = 3x + 4y$. Then

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Parallel

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(A) The given equation is $9x^2 + 24xy + 16y^2 + 21x + 28y + 6 = 0$.This can be written as $(3x + 4y)^2 + 7(3x + 4y) + 6 = 0$.Let $u = 3x + 4y$. Then the equation becomes $u^2 + 7u + 6 = 0$.Factoring the quadratic,we get $(u + 6)(u + 1) = 0$.Substituting back,we have $(3x + 4y + 6)(3x + 4y + 1) = 0$.This represents two lines: $3x + 4y + 6 = 0$ and $3x + 4y + 1 = 0$.Since the coefficients of $x$ and $y$ are the same in both equations,the lines are parallel.

The lines represented by the equation $9x^2 + 24xy + 16y^2 + 21x + 28y + 6 = 0$ are

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