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

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 

The straight line is x + y = 0, 3x + y – 4 = 0 and x + 3y – 4 = 0 from a triangle which 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 straight lines 4x – 3y – 5 = 0, x – 2y – 10 = 0, 7x + 4y – 40 = 0 and x + 3y + 10 = 0 form the sides of a

If two vertices of a triangle are (5, –1) and (–2, 3), and the orthocenter lies at the origin, the coordinate of the third vertex are 

Equation of a line passing through the intersection of the lines

x + 2y – 10 = 0 and 2x + y + 5 = 0 is 

 The lengths of the perpendicular from the points (m², 2m), (mm’, m +m’) and (m’², 2m’) to the line x + y + 1 = 0 form