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There are eight lines in a plane, no two of which are parallel. What is the maximum number of points at which they can intersect?

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Important Questions on Straight Lines

HARD
O (0, 0), A (1, 2), B (3, 4) are the vertices of OAB. The joint equation of the altitude and median drawn from O is
EASY
The graph of the equation x-7y=-42 intersects the y-axis at Pα,β and the graph of 6x+y-15=0, intersects the x-axis at Qγ,δ. What is the value of α+β+γ+δ?
HARD
If the straight line 2x-3y+17=0 is perpendicular to the line passing through the points 7,17 and 15, β, then β equals :
HARD
The tangent to the curve y=x2-5x+5, parallel to the line 2y=4x+1, also passes through the point :
EASY
Find the y-intercept of the line joining two points (1, 3) and (3, 5).
MEDIUM
Two vertices of a triangle are 0,2 and 4,3. If its orthocenter is at the origin, then its third vertex lies in which quadrant?
EASY
The equation of the line passing through the point -3,1 and bisecting the angle between coordinate axes is
HARD
Let L be the line passing through the point P1,2 such that its intercepted segment between the co-ordinate axes is bisected at P. If L1 is the line perpendicular to L and passing through the point -2, 1, then the point of intersection of L and L1 is
EASY

Answer the question on the basis of the following figure.

If AB is parallel to EC and BCD=72°, what will be that value of BAC?

Question Image

 

MEDIUM
If S1 and S2 are two straight lines such that the reflection of S1 in S2 and the reflection of S2 in S1 coincide, the angle between S1 and S2 is equal to?
MEDIUM

The number of values of k, for which the system of equations :

k+1x+8y=4k

kx+k+3y=3k-1

has no solution, is :
EASY
The y-intercept of the line passing through A6,1  and perpendicular to the line x-2y=4 is …
MEDIUM
A ray of light along x+3y=3 gets reflected upon reaching X-axis, the equation of the reflected ray is
MEDIUM
Two sides of a parallelogram are along the lines, x+y=3 and x-y+3=0. If its diagonals intersect at 2,4, then one of its vertex is:
HARD
A straight line L through the point (3, -2) is inclined at an angle of 60° to the line 3x+y=1. If L also intersects the X-axis, then the equation of L is:
EASY
Distance between two parallel lines y=2x+4 and y=2x-1 is
MEDIUM
Let a, b, c and d be non-zero numbers. If the point of intersection of the lines 4ax+2ay+c=0 & 5bx+2by+d=0 lies in the fourth quadrant and is equidistant from the two axes then 
HARD
A ray of light passing through the point (1,2) reflects on the X -axis at point A and the reflected ray passes through the point (5,3) . The coordinate of A is
EASY
The two equations are 4x + 4ky - 6 = 0 and x + 6y - 12 = 0. Find the value of k for which the pair of two linear equations represents the parallel lines.
MEDIUM
A rectangle is inscribed in a circle with a diameter lying along the line 3y=x+7. If the two adjacent vertices of the rectangle are -8, 5 and 6, 5, then the area of the rectangle (in sq. units) is: