Straight Lines — Class 12 Mathematics PYQs

What is the equation to the straight line passing through the point
$(-\sin \theta ,\cos \theta )$ and perpendicular to the line $x\cos \theta +y\sin \theta =9$?

Two points $P$ and $Q$ lie on line
$y=2x+3$. These two points $P$ and $Q$ are at a distance $2$ units from another point $R(1,5)$. What are the coordinates of the points $P$ and $Q$?

If two sides of a square lie on the lines
$2x+y-3=0$ and $4x+2y+5=0$, then what is the area of the square in square units?

Consider the following for the next two (02) items that follow :

A quadrilateral is formed by the lines $x=0,y=0,x+y=1$ and $6x+y=3$.

What is the equation of diagonal through origin?

Consider the following for the next two (02) items that follow :

A quadrilateral is formed by the lines $x=0,y=0,x+y=1$ and $6x+y=3$.

What is the equation of other diagonal?

Given that $16p^2+49q^2-4r^2-56pq=0$. Which one of the following is a point on a pair of straight lines $(px+qy+r)(px+qy-r)=0$ ?

For what values of $k$ is the line $(k-3)x-(5-k^2)y+k^2-7k+6=0$ parallel to the line $x+y=1$ ?

The line $x+y=4$ cuts the line joining $P(-1,1)$ and $Q(5,7)$ at $R$. What is $PR:RQ$ equal to ?

What is the sum of the intercepts of the line whose perpendicular distance from origin is $4$ units and the angle which the normal makes with positive direction of x-axis is $15^{\circ }$ ?

Consider the inequations
$5x-4y+12<0$, $x+y<2$, $x<0$ and $y>0$. Which one of the following points lies in the common region ?