(D) The given equation is $x^2 + xy + y^2 = 0$. Comparing this with the general form $ax^2 + 2hxy + by^2 = 0$,we have $a = 1$,$2h = 1$,and $b = 1$. Th

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(D) The given equation is $x^2 + xy + y^2 = 0$. Comparing this with the general form $ax^2 + 2hxy + by^2 = 0$,we have $a = 1$,$2h = 1$,and $b = 1$. The nature of the lines is determined by the discriminant $h^2 - ab$. Here,$h = 1/2$,so $h^2 - ab = (1/2)^2 - (1)(1) = 1/4 - 1 = -3/4$. Since $h^2 - ab < 0$,the lines represented by the equation are imaginary.

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

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The two lines represented by the equation $x^2 + xy + y^2 = 0$ are

A
Coincident
B
Parallel
C
Mutually perpendicular
D
Imaginary

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Pair of straight lines

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Equation of pair of straight lines

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EasyMHT CET 2022

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The two lines represented by the equation $x^2 + xy + y^2 = 0$ are

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If $ax^2 - y^2 + 4x - y = 0$ represents a pair of lines,then $a = $

If $L{x^2} - 10xy + 12{y^2} + 5x - 16y - 3 = 0$ represents a pair of straight lines,then the value of $L$ is:

The equation of the line common to the pair of lines $(p^2-q^2) x^2+(q^2-r^2) xy+(r^2-p^2) y^2=0$ and $(l-m) x^2+(m-n) xy+(n-l) y^2=0$ is

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