Dr. SK Goyal Solutions for Chapter: Pair of Straight Lines, Exercise 9: Multiple Choice II

If the two lines represented by $x^2\left({\tan }^2\theta +{\cos }^2\theta \right)-2xy\tan \theta +y^2{\sin }^2\theta =0$ make angles $\alpha ,\beta$ with the $x$-axis, then :

The equation $a{x}^2+b{y}^2+cx+cy=0$ represents a pair of straight lines, if :

If $x^2+\alpha y^2+2\beta y=a^2$ represents a pair of perpendicular straight lines, then :

Two pair of straight lines have the equations $y^2+xy-12x^2=0$ and $a{x}^2+2hxy+b{y}^2=0$. One line will be common among them, if :

If angle between the lines $x^2-xy+a{y}^2=0$ is $45°$, then value(s) of $a$ is/are:

Equation of pair of lines passing through $\left(1,-1\right)$ and parallel to the lines $2x^2+5xy+3y^2=0$ is :

The pair of lines represented by $3a{x}^2+5xy+\left(a^2-2\right)y^2=0$ and at right angles to each other, then value (s) of $a$ is/are :

If the pair of lines $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ intersect on $y$-axis, then :