Vinod Singh and Shweta Pawar Solutions for Chapter: Pair of Straight Lines, Exercise 2: Critical Thinking

If the pair of lines $x^2+2xy+a{y}^2=0$ and $a{x}^2+2xy+y^2=0$ have exactly one line in common, then the joint equation of the other two lines is given by

If one of the line represented by the equation $a{x}^2+2hxy+b{y}^2=0$ is coincident with one of the line represented by $a^{\text{'}}{x}^2+2h^{\text{'}}xy+b^{\text{'}}{y}^2=0$, then

If the sum of the slopes of the lines represented by the equation $x^2-2xy\tan A-y^2=0$ be $4$, then $\angle A=$

If slope of one of the lines $a{x}^2+2hxy+b{y}^2=0$ is $5$ times that of the other, then $5h^2=$

The condition that the gradient of one line is twice the gradient of another line represented by the equation $a{x}^2+2hxy+b{y}^2=0$ is

If the slope of one of the line represented by the equation $a{x}^2+2hxy+b{y}^2=0$ be $\lambda$ times that of the other, then

If the slope of one of the lines represented by $a{x}^2+2hxy+b{y}^2=0$ be the square of the other, then

If $m_1,m_2$ are slopes of lines represented by $2x^2-5xy+3y^2=0$, then equation of lines passing through origin with slopes $\frac{1}{m_1},\frac{1}{m_2}$ will be