List of top Mathematics Questions on Intersecting Lines

Let O be the vertex of the parabola \(y^2 = 4x\) and its chords OP and OQ are perpendicular to each other. If the locus of the mid-point of the line segment PQ is a conic C, then the length of its latus rectum is:
From the point $(-1, -1)$, two rays are sent making angles of $45^\circ$ with the line $x+y=0$. These rays get reflected from the mirror $x+2y=1$. If the equations of the reflected rays are $ax+by=9$ and $cx+dy=7$, $a, b, c, d \in \mathbb{Z}$, then the value of $ad+bc$ is :}
Let \( A \) be the point of intersection of the lines \( 3x + 2y = 14 \), \( 5x - y = 6 \) and \( B \) be the point of intersection of the lines \( 4x + 3y = 8 \), \( 6x + y = 5 \). The distance of the point \( P(5, -2) \) from the line \( AB \) is
The points of intersection of the lines 2x+3y-5=0 and 3x-4y+1=0 lies in which quadrant ?
The maximum number of points into which 4 circles and 4 straight lines intersect, is
Use the figure to name : 
Line containing point E
(a) Line containing point E. 
(b) Line passing through A. 
(c) Line on which O lies 
(d) Two pairs of intersecting lines.

Draw a rough figure and label suitably in each of the following cases:
(a) Point P lies on AB.
(b) XY s ruu and PQ s ruu intersect at M.
(c) Line l contains E and F but not D.
(d) OP s ruu and OQ s ruu meet at O.