Straight Line a...

If the lines represented by the equation 2x² – 3xy + y² = 0 make angles α and β with x-axis, then cot² α + cot² β

Angle between the lines joining the origin to the points of intersection of the curves 2x² + 3y² + 10x = 0 and 3x² + 5y² + 16x = 0 is

The lines (lx + my)² – 3(mx – ly)² = 0 and lx + my + n = 0 form

If (a + 3b)(3a + b) = 4h², then the angle between the lines represented by ax² + 2hxy + by² = 0 is

The angle between the lines represented by the equation (x² + y²) sin θ + 2xy = 0 is

The straight lines joining the origin to the points of intersection of the line 2x + y = 1 and curve 3x² + 4xy – 4x + 1 = 0 include an angle

If two of the three lines represented by the equation ax³ + bx²y + cxy² + dy³ = 0 are perpendicular, then

The acute angle formed between the lines joining the origin to the points of intersection of the curves x² + y² – 2x –1 = 0 and x + y = 1, is

If the angle 2θ is acute, then the acute angle between x² (cos θ – sin θ) + 2xy cos θ + y² (cos θ + sin θ) = 0 is