Pair of straight lines practice · Easy

The distance between the pair of lines represented by the equation ${x^2} - 6xy + 9{y^2} + 3x - 9y - 4 = 0$ is

Separate equations of lines for a pair of lines whose equation is ${x^2} + xy - 12{y^2} = 0$, are

If the equation of the pair of straight lines passing through the point $(1,1)$, one making an angle $\theta$ with the positive direction of the $X$-axis and the other making the same angle with the positive direction of the $Y$-axis, is $x^2-(a+2) x y+y^2+a(x+y-1)=0, a \neq-2$, then the value of $\sin 2 \theta$ is

The distance between the pair of parallel lines ${x^2} + 4xy + 4{y^2} + 3x + 6y - 4 = 0$ is

If the equation $x^2+(\lambda+\mu) x y+\lambda \mu y^2+x+\mu y=0$ represents two parallel straight lines, then

If $a{x^2} - {y^2} + 4x - y = 0$ represents a pair of lines, then $a$ is equal to

The difference of the tangents of the angles which the lines $x^2\left(\sec ^2-\sin ^2 \theta\right)-2 x y \tan \theta+y^2 \sin ^2 \theta=0$ make with $\mathrm{X}$-axis, is

The lines joining the points of intersection of line $x+y=1$ and curve $x^2+y^2-2 y+\lambda=0$ to the origin are perpendicular, then the value of $\lambda$ will be

If the slope of one line in the pair $a x^2+4 x y+y^2=0$ is three times the other, then $a=$

The combined equation of the lines $l_1$ and $l_2$ is $2 x^2+6 x y+y^2=0$ and that of the lines $m_1$ and $m_2$ is $4 x^2+18 x y+y^2=0$. If the angle between $l_1$ and $m_2$ is $\alpha$, then the angle between $l_2$ and $m_1$ will be

Given the four lines with the equations

$x+2 y-3=0,3 x+4 y-7=0,$

$2 x+3 y-4=0,4 x+5 y-6=0, \text { then }$

The angle between the lines represented by $x^2+2 x y \sec \theta+y^2=0$, is

A line perpendicular to the line segment joining the points $(7,3)$ and $(3,7)$ divides it in the ratio $1: 3$, the equation of the line is

The product of the perpendiculars drawn from the point $(1,2)$ to the pair of lines $x^2+4 x y+y^2=0$ is

The distance between the pair of parallel lines ${x^2} + 2xy + {y^2} - 8ax - 8ay - 9{a^2} = 0$ is

If the equation $6 x^2-5 x y+y^2=0$ represents a pair of distinct straight lines each passing through the origin. Then, the separate equation of these lines are

If the slope of one of the lines given by $6 x^2+a x y+$ $y^2=0$ exceeds the slope of the other by one, then $a$ is equal to

If the distance of a point $\left(x_1, y_1\right)$ from each of the two straight lines, which pass through the origin of coordinates, is $\delta$, then the two lines are given by

The angle between the pair of lines represented by $2 x^2-7 x y+3 y^2=0$, is

The combined equation of the bisectors of the angle between the lines represented by $\left(x^2+y^2\right) \sqrt{3}=4 x y$ is

The triangle formed by the lines whose combined equation is $\left(y^2-4 x y-x^2\right)(x+y-1)=0$, is

If the bisectors of angles represented by $a{x^2} + 2hxy + b{y^2} = 0$ and $a'{x^2} + 2h'xy + b'{y^2} = 0$ are same, then

If the equation $3{x^2} + xy - {y^2} - 3x + 6y + k = 0$ represents a pair of straight lines, then the values of $k$ is

The equation of a line in parametric form is given by

If two of the lines given by the equation $a{y^4} + bx{y^3} + c{x^2}{y^2} + d{x^3}y + e{x^4} = 0$ are at right angle, then

If the sum of the slopes of the lines given by $3 x^2-2 c x y-5 y^2=0$ is twice their product, then the value of $c$ is

If the equation $x^4+b x^3 y+c x^2 y^2+d x y^3+e y^4=0$ represents two pairs of perpendicular lines, then

The point of intersection of the pair of straight lines given by $6 x^2+5 x y-4 y^2+7 x+13 y-3=0$, is

If the slopes of the lines given by $a x^2+2 h x y+b y^2=0$ are in the ratio $3: 1$, then $h^2=$

If the equation $4{x^2} + hxy + {y^2} = 0$ represent coincident lines, then $h$ is equal to