Question

If p1p2 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

Solution

Correct option is

4 cosec2 4α

                    

SIMILAR QUESTIONS

Q1

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 

Q2

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  

Q3

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 

Q4

The straight line is x + y = 0, 3x + y – 4 = 0 and x + 3y – 4 = 0 from a triangle which is  

Q5

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

Q6

If the line 2 (sin a + sin bx – 2 sin (a – by = 3 and 2 (cos a + cos bx + 2 cos (a – by = 5 are perpendicular, then sin 2a+ sin2b is equal to     

 

Q7

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

Q8

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

Q9

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 

Q10

 

Equation of a line passing through the intersection of the lines

x + 2y – 10 = 0 and 2x + y + 5 = 0 is