Dr. SK Goyal Solutions for Chapter: Pair of Straight Lines, Exercise 4: INTRODUCTORY EXERCISE 3.4

If $\lambda x^2+10xy+3y^2-15x-21y+18=0$ represents a pair of straight lines. Then the value of $\lambda$ is:

The point of intersection of the straight lines given by the equation $3y^2-8xy-3x^2-29x+3y-18=0$ is:

If the equation $12x^2+7xy-p{y}^2-18x+qy+6=0$ represents two perpendicular lines, then the value of $p$ and $q$ are :

Find the area of the parallelogram formed by the lines
$2x^2+5xy+3y^2=0$ and $2x^2+5xy+3y^2+3x+4y+1=0$

Find the locus of the incentre of the triangle formed by
$xy-4x-4y+16=0$ and $x+y=a$
($a>4,a\ne 4\sqrt{2}$ and $a$ is the parameter)

If the equation $2hxy+2gx+2fy+c=0$ represents two straight lines, show that they form a rectangle of area $\frac{\left|fg\right|}{h^2}$ with the co-ordinate axes.

Find the area of the triangle formed by the lines represented by $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ and axis of $x$.

Find the equations of the straight lines passing through the point $\left(1,1\right)$ and parallel to the lines represented by the equation $x^2-5xy+4y^2+x+2y-2=0$.