Pair of Straight Lines

Homogenize $y^2=x$ with $x+y=2$.

Find the angle between the lines joining the origin to the points of intersection of $y^2=x$ and $x+y=1$.

If the lines $x^2+(1-k)xy-3y^2=0$ are equally inclined to co-ordinate axes, then find the value of $k$.

If the lines $x^2+(2+k)xy-4y^2=0$ are equally inclined to co-ordinate axes, then find the value of $k$.

If the equation $a{x}^2+b{y}^2+cx+cy=0,c\ne 0$ represents a pair of lines, then

If the angle between the lines given by the equation $x^2-3xy+\lambda y^2+3x-5y+2=0, \lambda \ge 0,$ is ${\tan }^{-1}\left(\frac{1}{3}\right),$ then $\lambda =$

If the equation $kxy+5x+3y+2=0$ represents a pair of lines, then $k=$

The values of $\mathrm{\lambda }$ for which the equation ${\mathrm{x}}^2-{\mathrm{y}}^2-\mathrm{x}-\mathrm{\lambda y}-2=0$ represents a pair of straight lines are :

Consider a pair of perpendicular straight lines $a{x}^2+3xy-2y^2-5x+5y+c=0$. The value of $a$ is:

If lines represented by $\left(1+\mathrm{s}\mathrm{i}{\mathrm{n}}^2\theta \right)x^2+2hxy+2\mathrm{s}\mathrm{i}\mathrm{n}\theta y^2=0,\theta \in \left[\mathrm{0,2}\pi \right]$ are perpendicular to each other then $\theta$ = ….

Figure shows a square ABCD of side length unity whose diagonal's end points B and D are resting on x-axis and y-axis respectively as shown in figure. If vertices B and D starts to slide along x-axis and y-axis then vertices A and C moves on ax² + 2hxy + by² = 0. The value of a + h + b is:

The line $x+y=k$ meets the pair of straight lines $x^2+y^2-2x-4y+2=0$ in two points $A$ and $B$. If $O$ is the origin and $\angle AOB=90°$ then the value of $k>1$ is

The angle between the lines $x^2-xy-6y^2-7x+31y-18=0$ is

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

Pair of straight lines perpendicular to each other represented by

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

The angle between the pair of straight lines $x^2-y^2-2y-1=0$ , is

$2x^2+7xy+3y^2+8x+14y+\lambda =0$

will represent a pair of straight lines, when $\lambda =$

A value of $\lambda$ for which the equation $x^2-\lambda xy+2y^2+3x-5y+2=0$ may represent a pair of straight lines is

If the equation $a{x}^2+b{y}^2+cx+cy=0$ represents a pair of straight lines, then