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The equation of bisectors of the angles between the lines |x| = |y| are

The area of the parallelogram formed by the lines y = mx, y = mx + 1, y = nx and y = nx + 1 equals

A point starts moving from (1,2) and its projection on x and y-axis are moving with velocities of 3m/s and 2m/s respectively. Its locus is

The lines p(p² + 1) x – y + q = 0 and (p² + 1)² x + (p² + 1)y + 2q = 0 are perpendicular to a common line for

The equation of the locus of the point of intersection of the straight lines x sin θ + (1 – cos θ) y = a sin θ and x sin θ – (1 + cos θ)y + a sin θ = 0 is

If P is a point (x,y) on the line y = –3x such that P and the point (3,4) are on the opposite sides of the line 3x – 4y – 8 = 0, then

If the equations of opposite sides of a parallelogram are x² – 7x + 6 = 0 and y² – 14y + 40 = 0, then the equation of its one diagonal is

The image of the pair of lines represented by ax² + 2hxy + by² = 0 by the line mirror y = 0 is

If the portion of the line lx + my = 1 falling inside the circle x² + y² = a² subtends an angle of 450 at the origin, then