R D Sharma Solutions for Chapter: The Straight Lines, Exercise 20: VERY SHORT ANSWER QUESTIONS (VSAQs)

Write an equation representing a pair of lines through the point $(a,b)$ and parallel to the coordinate axes.

Write the value of $\theta \in (0 , \frac{\pi }{2})$ for which area of the triangle formed by points $O(0,0), A(a \cos \theta , b \sin \theta )$ and $B(a \cos \theta ,-b \sin \theta )$ is maximum.

Write the area of the triangle formed by the coordinate axes and the line $(\sec \theta -\tan \theta )x+(\sec \theta +\tan \theta )y=2$.

If the diagonals of the quadrilateral formed by the lines $l_{1}x+m_{1}y+n_1=0, l_{2}x+m_{2}y+n_2=0, l_{1}x+m_{1}y+n_1^{\text{'}}=0$ and $l_{2}x+m_{2}y+n_2^{\text{'}}=0$ are perpendicular, then write the value of $l_1^2-l_2^2+m_1^2-m_2^2$.

Write the sum of the coordinates of the image of the point $(3,8)$ in the line $x+3y-7=0$.

Write the integral values of $m$ for which the $x$ -coordinate of the point of intersection of the lines $y=mx+1$ and $3x+4y=9$ is an integer.

If $a\ne b\ne c$, write the condition for which the equations $(b-c) x+(c-a) y+(a-b)=0$ and $\left(b^3-c^3\right)x+\left(c^3-a^3\right)y+\left(a^3-b^3\right)=0$ represent the same line.

If $a, b, c$ are in G.P. write the area of the triangle formed by the line $ax+by+c=0$ with the coordinates axes.