(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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(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.

Class 11 Mathematics Pair of straight lines Equation of pair of straight lines

Medium

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

A
Real and coincident
B
Real and different
C
Imaginary and different
D
None of the above

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Equation of pair of straight lines

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

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