General Second Degree Equations in Two Variables

If $\varphi$ is the acute angle between the lines given by $3x^2-4xy+b{y}^2=0$ and $\tan \varphi =\frac{1}{2}$ then $b=$

Value of $k$ for which $12x^2-10xy+2y^2+11x-5y+k=0$ represents a pair of straight lines is

Find the value of $\lambda$ for which $2x^2+7xy+3y^2+8x+14y+\lambda =0.$

The pair of lines given by the equation $4x^2+8xy-3y^2=0$ are

The line $y=3x$ bisects the angle between the lines $a{x}^2+2axy+y^2=0$ if $a=?$

Equation of all lines passing through the intersection of lines $2x+3y=5$ and $x+y=2$ is given by $(2x+3y-5)+\lambda (x+y-2)=0$, of all these lines one line is farthest from point $(7,4)$, the value of $\lambda$ is :

The equation $x^2-y^2+ax+b=0$ represents a pair of lines for the ordered pair $\left(a,b\right)=$

If the lines represented by $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ intersect on the $\mathrm{x}$-axis, which of the following is in general incorrect

Let $a$ and $b$ be non-zero real numbers. Then, the equation $\left(a{x}^2+b{y}^2+c\right)\left(x^2-5xy+6y^2\right)=0$ represents 

The combined equation of the pair of line passing through $(-1,2)$, one is parallel to $x+3y-1=0$ and other is perpendicular to $2x-3y-1=0$ is

If one of the lines given by the equation $2x^2+axy+3y^2=0$ coincide with one of those given by the equation $2x^2+bxy-3y^2=0$, while the other two lines are perpendicular to each other, then the values of $a$ and $b$ are

If the equation $2x^2+kxy-6y^2+3x+y+1=0, \left(k>0\right)$ represents a pair of straight lines, then their point of intersection is

Find the length of the intercept cut by the pair of lines $2x^2+4xy-4y^2-6x-8y+7=0$ over the $y$-axis.

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

The angle between lines represented by $\left({\sin }^2\alpha \right)y^2-2xy\left({\cos }^2\alpha \right)+\left({\cos }^2\alpha -1\right)x^2=0$ is

The distance between pair of parallel lines represented by $x^2+2xy+y^2-8ax-8ay-9a^2=0$ is _____ units

If $a{x}^2+6\mathrm{xy}+b{y}^2-10\mathrm{x}+10\mathrm{y}-6=0$ represents a pair of perpendicular lines then the value of $\left|a\right|$ equals $\_\_\_\_\_\_\_\_\_$

The value of $\lambda$, for which the equation $x^2-y^2-x+\lambda y-2=0$represents a pair of straight lines, are

The lines represented by the equation $x^2+2\sqrt{3}xy+3y^2-3x-3\sqrt{3}y-4=0$, are

If $\theta$ is the angle between the pair of straight lines $x^2-5xy+4y^2+3x-4=0$$,$ then ${\tan }^2\theta$ is equal to