The Straight Line Is x + y = 0, 3x + y – 4 = 0 And x + 3y – 4 = 0 From A Triangle Which Is  

If θ is an angle between the lines given by the equation 6x² + 5xy – 4y² + 7x + 13y – 3 = 0, then equation of the line passing through the point of intersection of these lines and making an angle θ with the positive x-axis is 

If one of the lines given by the equation 2x² + axy + 3y² = 0 coincide with one of those given by 2x² + bxy – 3y² = 0 and the other lines represented by them be perpendicular, then 

The equation x – y = 4 and x² + 4xy + y² = 0 represent the sides of  

If the equation of the pair of straight lines passing through the point (1, 1), one making an angle θ with the positive direction of x-axis and the other making the same angle with the positive direction of y-axis is x² – (a + 2)xy + y² + a(x + y – 1) = 0,  

a ≠ –2, then the value of sin 2θ is 

If θ₁ and θ₂ be the angles which the lines (x² + y²) (cos² θ sin²α + sin² θ) = (x tan α – y sin θ)² make with axis ofx, then if θ = π/6,

tan θ₁ + tan θ₂ is equal to  

If two of the lines represented by  

                      x⁴ + x³ y + cx² y² – xy³ + y⁴ = 0  

bisect the angle between the other two, then the value of c is 

 If the line x + 2ay + a = 0, x + 3by + b = 0 and x + 4cy + c = 0 are concurrent, then a, b, c are in

If the line 2 (sin a + sin b) x – 2 sin (a – b) y = 3 and 2 (cos a + cos b) x + 2 cos (a – b) y = 5 are perpendicular, then sin 2a+ sin2b is equal to     

If p₁, p₂ denote the lengths of the perpendiculars from the origin on the lines x sec α + y cosec α = 2a and

x cos α + y sin α = a cos 2α respectively, then  is equal to

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