Amit M Agarwal Solutions for Chapter: Straight Line and Pair of Straight Lines, Exercise 5: Target Exercises

If one of the lines of the pair $a{x}^2+2hxy+b{y}^2=0$ bisects the angles between positive directions of the axes, then $a,b$ and $h$ satisfy the relation

If the straight lines $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ intersect on the $X-$axis, then

The four straight lines given by the equations $12x^2+7xy-12y^2=0$ and $12x^2+7xy-12y^2-x+7y-1=10$ lie along the sides of a
 

Area of the triangle formed by the lines $y^2-9xy+18x^2=0$ and $y=9,$ is

The area of the triangle formed by the lines $4x^2-9xy-9y^2=0$ and $x=2$ is equal to

The value of $\lambda$ for which the lines joining the point of intersection of curves $C_1$ and $C_2$ to the origin are equally inclined to the $X$-axis, where $C_1:\lambda x^2+3y^2-2\lambda xy+9x=0$ and $C_2:3x^2-4y^2+8xy-3x=0,$ is

The area of the triangle formed by joining the origin to the points of intersection of the line $\sqrt{5}x+2y=3\sqrt{5}$ and circle $x^2+y^2=10$, is

If the lines joining origin to the points of intersection of the line $fx-gy=\lambda$ and the curve $x^2+hxy-y^2+gx+fy=0$ are mutually perpendicular, then