The nature of the straight lines represented | vedclass

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(A) The given equation is $4x^2 + 12xy + 9y^2 = 0$.Comparing this with the general homogeneous equation of the second degree $ax^2 + 2hxy + by^2 = 0$,

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Real and coincident

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(A) The given equation is $4x^2 + 12xy + 9y^2 = 0$.Comparing this with the general homogeneous equation of the second degree $ax^2 + 2hxy + by^2 = 0$,we get $a = 4$,$2h = 12$ (so $h = 6$),and $b = 9$.The nature of the lines is determined by the value of $h^2 - ab$.Calculating $h^2 - ab = (6)^2 - (4)(9) = 36 - 36 = 0$.Since $h^2 - ab = 0$,the lines represented by the equation are real and coincident.

The nature of the straight lines represented by the equation $4x^2 + 12xy + 9y^2 = 0$ is

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