Straight Line a...

If the pair of lines ax² + 2hxy + by² + 2gx + 2fy + c = 0 intersect on the y-axis, then

The equation of the locus of foot of perpendiculars drawn from the origin to the line passing through a fixed point (a,b) is

The equations to a pair of opposite sides of a parallelogram are x² – 5x + 6 = 0 and y² – 6y + 5 = 0. The equations to its diagonals are

Area of the triangle formed by the lines y² – 9xy + 18x² = 0 and y = 9 is

The area (in square units) of the quadrilateral formed by the two pairs of lines
l² x² – m² y² – n(lx + my) = 0 and
l² x² – m² y² + n(lx – my) = 0 is

The equation of the pair of straight lines, each of which makes an angle α with the line y = x, is

The figure formed by the lines x² + 4xy + y² = 0 and x – y = 4 is