A straight line through the point (2, 2) intersects the lines `sqrt3 x + y = 0` and `sqrt3 x - y = 0` at the points A and B. The equation of AB so that the triangle OAB is equilateral, where O is the origin.

Find the equation of the line through the intersection of the lines 3x+2y +5 = 0 and 3x - 4y +6 = 0 and the point (1,1)

The angle between the lines sqrt3 x – y–2 = 0 and x – sqrt3 y+1=0 is

Find the equation of the line through the intersection of the lines 3x + 2y + 5 = 0 and 3x - 4y + 6 = 0 and the point (1,1)

Find angle between the lines y - sqrt3x - 5 0 " and " sqrt3 y - x +6 = 0 .

A straight line L through the point (3,-2) is inclined at an angle 60^@ to the line sqrt(3)x+y=1 If L also intersects the x-axis then the equation of L is

A straight line passes through the point of Intersection of the lines x- 2y - 2 = 0 and 2x - by - 6= 0 and the origin, then the set of values of 'b' for which the acute angle between this line and y=0 is less than 45^@ is

If the point 3x+4y-24=0 intersects the X -axis at the point A and the Y -axis at the point B , then the incentre of the triangle OAB , where O is the origin, is

A straight line through the origin 'O' meets the parallel lines 4x +2y= 9 and 2x +y=-6 at points P and Q respectively. Then the point 'O' divides the segment PQ in the ratio

A line passes through the point of intersection of the lines 100x + 50y-1=0 and 75x + 25y + 3 = 0 and makes equal intercepts on the axes. Its equation is