(A) The general equation of a pair of straight lines passing through the origin is given by $ax^2 + 2hxy + by^2 = 0$. The lines are perpendicular if t

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(A) The general equation of a pair of straight lines passing through the origin is given by $ax^2 + 2hxy + by^2 = 0$. The lines are perpendicular if the sum of the coefficients of $x^2$ and $y^2$ is zero,i.e.,$a + b = 0$. For option $A$: $2x^2 = 4xy + 2y^2 \Rightarrow 2x^2 - 4xy - 2y^2 = 0$. Here,$a = 2$ and $b = -2$. Since $a + b = 2 + (-2) = 0$,the lines represented by this equation are perpendicular to each other.

Class 11 Mathematics Pair of straight lines Angle between the pair of straight lines, Condition for parallel and perpendicular lines

Medium

Which of the following equations represents a pair of straight lines perpendicular to each other?

A
$2{x^2} = 2y(2x + y)$
B
${x^2} + {y^2} + 3 = 0$
C
$2{x^2} = y(2x + y)$
D
${x^2} = 2(x - y)$

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Pair of straight lines

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Angle between the pair of straight lines, Condition for parallel and perpendicular lines

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If the lines $x^2+kxy+y^2=0$ and $x+y=1$ form the sides of an equilateral triangle,then the value of $k^2$ is

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Which of the following equations represents a pair of straight lines perpendicular to each other?

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