(A) The general equation of a pair of straight lines is given by $ax^2 + 2hxy + by^2 = 0$. For the lines to be perpendicular,the condition is $a + b =

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(A) The general equation of a pair of straight lines is given by $ax^2 + 2hxy + by^2 = 0$. For the lines to be perpendicular,the condition is $a + b = 0$. In option $A$,the equation is $-x^2 + xy + y^2 = 0$. Here,$a = -1$ and $b = 1$. Since $a + b = -1 + 1 = 0$,the lines represented by this equation are perpendicular.

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

Easy

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

A
$y^2 + xy - x^2 = 0$
B
$y^2 - xy + x^2 = 0$
C
$x^2 + xy + y^2 = 0$
D
$x^2 + xy - 2y^2 = 0$

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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

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

Medium

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If the acute angles between the pairs of lines $3x^2 - 7xy + 4y^2 = 0$ and $6x^2 - 5xy + y^2 = 0$ are $\theta_1$ and $\theta_2$ respectively,then:

Medium

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If the pair of straight lines given by $A x^2+2 H x y+B y^2=0$,where $(H^2>A B)$,forms an equilateral triangle with the line $a x+b y+c=0$,then $(A+3 B)(3 A+B)=$ (in $H^2$)

DifficultAP EAMCET 2020

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If the angle between the two lines represented by $2x^2 + 5xy + 3y^2 + 6x + 7y + 4 = 0$ is $\tan^{-1} m$,then $m = $

Medium

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The angle between the lines represented by $ax^2 + 2hxy + by^2 = 0$ is:

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

Similar Questions

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

If the acute angles between the pairs of lines $3x^2 - 7xy + 4y^2 = 0$ and $6x^2 - 5xy + y^2 = 0$ are $\theta_1$ and $\theta_2$ respectively,then:

If the pair of straight lines given by $A x^2+2 H x y+B y^2=0$,where $(H^2>A B)$,forms an equilateral triangle with the line $a x+b y+c=0$,then $(A+3 B)(3 A+B)=$ (in $H^2$)

If the angle between the two lines represented by $2x^2 + 5xy + 3y^2 + 6x + 7y + 4 = 0$ is $\tan^{-1} m$,then $m = $

The angle between the lines represented by $ax^2 + 2hxy + by^2 = 0$ is:

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