Maharashtra Board Solutions for Chapter: Pair of Straight Lines, Exercise 3: Exercise 4.3

Show that the following equations represent a pair of lines. Find the acute angle between them.

$2x^2+xy-y^2+x+4y-3=0$

Find the separate equation of the lines represented by the following equations:

$10{\left(x+1\right)}^2+\left(x+1\right)\left(y-2\right)-3{\left(y-2\right)}^2=0$

Find the value of $k$ if the following equations represent a pair of lines:

$kxy+10x+6y+4=0$

Find the value of $k$ if the following equations represent a pair of lines:

$x^2+3xy+2y^2+x-y+k=0$

Find $p$ and $q$, if the equation $p{x}^2-8xy+3y^2+14x+2y+q=0$  represents a pair of perpendicular lines.

Find $p$ and $q$, if the equation $2x^2+8xy+p{y}^2+qx+2y-15=0$  represents a pair of parallel lines.

Equations of pairs of opposite sides of a parallelogram are $x^2-7x+6=0$ and $y^2-14y+40=0.$  Find the joint equation of its diagonals.
 

$∆OAB$ is formed by the lines $x^2-4xy+y^2=0$ and the line $AB.$ The equation of line  $AB$ is $2x+3y-1=0 .$  Find the equation of the median of the triangle drawn from the origin.