Pair of straight lines practice · Easy

The equation of the bisector of the acute angle between the lines $3x - 4y + 7 = 0$ and $12x + 5y - 2 = 0$ is

The sum of slopes of lines $3{x^2} + 5xy - 2{y^2} = 0$ is

The equation ${x^2} + {y^2} + 4x + 6y + 13 = 0$ represents

If the slope of one of the lines given by $a x^2+2 h x y+b y^2=0$ is 5 times the other, then

The equation $a x^2+2 h x y+a y^2=0$ represent a pair of coincident lines through the origin if

The equation $\lambda\left(x^3-3 x y^2\right)+y^3-3 x^2 y=0$ represents three straight lines passing through the origin such that

If the angle between the pair of straight lines represented by the equation $x^2-3 x y+\lambda y^2+3 x-5 y+2=0$, is $\tan ^{-1} 3$, where ' $\lambda$ ' is a non-negative real number. Then, $\lambda=$

The lines joining the origin to the points of intersection of $x^2+y^2+2 g x+c=0$ and $x^2+y^2+2 f y-c=0$ are at right angles, if

The equation $x^3+a x^2 y+b x y^2+y^3=0$ represents three straight lines, two of which are perpendicular, then the equation of the third line, is

A line passing through the point $P(2,3)$ meets the lines represented by $x^2-2 x y-y^2=0$ at the points $A$ and $B$ such that $P A \cdot P B=17$, the equation of the line is

A line which makes an acute angle $\theta$ with the positive direction of $x$-axis is drawn through the point $P$ $(3,4)$ to meet the lines $x=6$ and $y=8$ at $R$ and $S$ respectively then $R S=8-2 \sqrt{3}$, if

The angle between the pair of straight lines $x^2+4 y^2-7 x y=0$, is

The straight lines represented by $x^2+m x y-2 y^2+3 y-1=0$ meet at the point

The point of intersection of the two lines given by $2 x^2-5 x y+2 y^2+3 x+3 y+1=0$ is

The line $y=m x$ bisects the angle between the lines $a x^2+2 h x y+b y^2=0,$ if

The angle between the pair of straight lines $y^2 \sin ^2 \theta-x y \sin ^2 \theta+x^2\left(\cos ^2 \theta-1\right)=0$, is

The value of 'a' for which the lines represented by $a{x^2} + 5\;xy + 2\;{y^2} = 0$ are mutually perpendicular is

If the line represented by ${x^2} - 2\;pxy - {y^2} = 0$ are rotated about the origin through an angle $\theta$, one in clockwise direction and other in anti-clockwise direction, then the equation of the bisectors of the angle between the lines in the new position is

The distance between the parallel lines $9{x^2} - 6xy + {y^2} + 18x - 6y + 8 = 0,$ is

If the slope of one of the lines represented by $a x^2+$ $(3 a+1) x y+3 y^2=0$ be reciprocal of the slope of the other, then the slopes of the lines are

The equation $3 a x^2+9 x y+\left(a^2-2\right) y^2=0$ represents two perpendicular straight lines for

The angle between the pair of lines given by $3 x^2+5 x y-2 y^2+x+9 y-4=0$

The equation $x^3+y^3=0$ represents

The equation of the line whose perpendicular distance from the origin is 3 units and the angle which the normal makes with the positive direction of $x$-axis is $30^{\circ}$ is

The combined equation of the pair of lines through the point (1, 0) and parallel to the lines represented by $2{x^2} - xy - {y^2} = 0$ is

If $\theta$ is the acute angle between the lines given by $x^2-2 p x y+y^2=0$, then

The angle between the lines ${x^2} + 4xy + {y^2} = 0$ is

If the distance between the parallel lines $3 x+4 y+7=0$ and $a x+y+b=0$ is 1 , the integral value of $b$ is

The equation of the bisector of the acute angle between the line $3x - 4y + 7 = 0$ and $12x + 5y - 2 = 0$ is

The angle $\theta$ between the pairs of straight lines represented by $6 x^2-x y-12 y^2-8 x+29 y-14=0$ is such that $\tan \theta$ equals