Vinod Singh and Shweta Pawar Solutions for Chapter: Straight Line, Exercise 2: Critical Thinking

If the equation $y=mx+c$ and $x\cos \alpha +y\sin \alpha =p$ represents the same straight line, then

The ratio in which the line $3x+4y+2=0$, divides the distance between $3x+4y+5=0$ and $3x+4y-5=0,$ is

The diagonals of the parallelogram whose sides are $lx+my+n=0, lx+my+n^{\text{'}}=0, mx+ly+n=0, mx+ly+n^{\text{'}}=0$ include an angle

The ends of the base of an isosceles triangle are at $(2a,0)$ and $(0,a)$. The equation of one side is $x=2a$. The equation of the other side is

Equation of the line passing through the point $(-4,3)$ and the portion of the line intercepted between the axes which is divided internally in the ratio $5:3$ by this point, is

If the lines $ax+2y+1=0, bx+3y+1=0$ and $cx+4y+1=0$ are concurrent, then $a, b, c$ are in

The equations $(b-c)x+(c-a)y+(a-b)=0$ and $\left(b^3-c^3\right)x+\left(c^3-a^3\right)y+a^3-b^3=0$ where, $a\ne b\ne c$ will represent the same line, if

If $2p$ is the length of perpendicular from the origin to the line $\frac{x}{a}+\frac{y}{b}=1,$ then $a^2, 8p^2, b^2$ are in