Two Lines Represented By The Equation  are Rotated About The Point (1, 0), The Line Making The Bigger Angle With The Positive Direction Of The x-axis Being Turned By 45o in The Clockwise Sense And The Other Line Being Turned By 15o in The Anticlockwise Sense. The Combined Equation Of The Pair Of Lines Kin Their New Position Is    

The square of the distance between the origin and the point of intersection of the lines given by  

The centroid of the triangle whose three sides are given by the combined equation  

If first degree terms and constant term are to be removed from the equation , then the origin must be shifted at the point

The angle between the straight lines joining the origin to the points of intersection of  and 3x – 2y = 1 is

All chords of the curve  which subtend a right angle at the origin always pass through the point

If the pair of lines represented by   intersect on y-axis, then  

If the chord y = mx + 1 of the circle x² + y² = 1 subtends an angle of 45^oat the major segment of the circle, then m =

The straight lines represented by

The equation  of the image of the pair of rays  in the line mirror x= 1 is

The value of λ for which the lines joining the point of intersection of curves C₁ and C₂ to the origin are equally inclined to the axis of X.