If the point α , 7 3 3 lies on the curve traced by the mid-points of the line segments of the lines x cos θ + y sin θ = 7 , θ ∈ 0 , π 2 between the co-ordinates axes, then α is equal to

Step-by-step solution

The straight line is shown below with the intercepts. M 7 2 cos θ ,   7 2 sin θ ≡ h ,   k ∴   cos θ = 7 2 h         sin θ = 7 2 k ∵   θ ∈ 0 ,   π 2 ⇒ 49 4 h 2 + 49 4 k 2 = 1       ∴   x and y are positive ∴ Locus = 1 x 2 + 1 y 2 = 4 49 Now α ,   7 3 3 lies on curve ⇒ 1 α 2 + 9 147 = 4 49 1 α 2 = 1 49 ∴   α = ± 7 ∴   α