Dr. SK Goyal Solutions for Chapter: Pair of Straight Lines, Exercise 2: INTRODUCTORY EXERCISE 3.2

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

Which of the following pairs of straight lines intersect at right angles?

If $h^2=ab$, then the lines represented by $a{x}^2+2hxy+b{y}^2=0$ are :

Equation $a{x}^3-9x^{2}y-x{y}^2+4y^3=0$ represents three straight lines. If the two of the lines are perpendicular, then $a=$

Find the angle between the lines whose joint equation is $2x^2-3xy+y^2=0$

Show that the lines
$\left(1-\cos \theta \tan \alpha \right)y^2-\left(2\cos \theta +{\sin }^2\theta \tan \alpha \right)xy+\cos \theta \left(\cos \theta +\tan \alpha \right)x^2=0$ include an angle $\alpha$ between them.

Find the angle between the lines represented by the equation $x^2-2pxy+y^2=0$

Prove that the triangle formed by the lines $a{x}^2+2hxy+b{y}^2=0$ and $lx+my=1$ is isosceles, if $h\left(l^2-m^2\right)=\left(a-b\right)m$.