Vinod Singh and Shweta Pawar Solutions for Chapter: Pair of Straight Lines, Exercise 3: Competitive Thinking

The angle between the lines given by $x^2-xy-6y^2-7x+31y-18=0$ is

If the angle between the pair of straight lines represented by the equation $x^2-3xy+\lambda y^2+3x+5y+2=0$ is ${\tan }^{-1}3$ where $\lambda$ is a non-negative real number, then $\lambda =$

If the angle between the two lines represented by $2x^2+5xy+3y^2+6x+7y+4=0$ is ${\tan }^{-1}m,$ then $m=$

The straight lines joining the origin to the points of intersection of the line $2x+y=1$ and curve $3x^2+4xy-4x+1=0$ include an angle

The line joining origin and point of intersection of curves $a{x}^2+2hxy+b{y}^2+2gx=0$ and $a_1{x}^2+2h_{1}xy+b_1{y}^2+2g_{1}x=0$ will be mutually perpendicular if

The pair of straight lines joining the origin to the point of intersection of the line $y=2\sqrt{2}x+c$ and the circle $x^2+y^2=2$ are at right angle, if

The orthocenter of the triangle formed by the lines $x+y=1$ and $2y^2-xy-6x^2=0$ is

Two pairs of straight lines with combined equations $xy+4x-3y-12=0$ and $xy-3x+4y-12=0$ form a square. Then the combined equation of its diagonals is