Embibe Experts Solutions for Chapter: Pair of Straight Lines, Exercise 1: TS EAMCET - 5 August 2021 Shift 2

The angle by which axes are to be rotated without changing the origin so that the transformed equation of $x^2+4xy-y^2=0$ in new coordinates $\left(X, Y\right)$ does not contain $XY$ term is

The product of the length of perpendiculars from origin to the pair of lines $x^2+3y^2+4xy-4x-10y+3=0$ is

From the point $(3, -4)$ perpendicular lines $L_1$ and $L_2$ are drawn on each of the lines $S\equiv 2x^2+3xy-2y^2-7x+y+3=0.$ The area of the quadrilateral formed by the pair of lines $S=0,{ L}_1$ and $L_2$ is (in square units)

Consider the lines $L_1\equiv 4x+5y-6=0, L_2\equiv 2x+3y-4=0, L_3\equiv 3x-y+2=0.$ If the line $L_1=0$ intersects the lines $L_2=0$ and $L_3=0$ at the points $A$ and $B$ respectively, then the combined equation of $OA$ and $OB$ is

The equation $3a{x}^2-16xy-\left(a^2-10\right)y^2=0$ represents

The angle between the pair of straight lines $3y^2-8xy-3x^2-29x+3y-18=0$ is

The line $\frac{x}{3}+\frac{y}{2}=1$ and a pair of lines both passing through origin forms an isosceles triangle. If this pair of lines are perpendicular, then the equation of the pair of straight lines is

If $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ represents a pair of lines, which of the following statements is true?