Distance of all the points from (0, 0) are 5 units. That means circumcentre of the triangle formed by the given point is (0, 0) if G(h,k) be the centroid of triangle, then 3h = 3 + 5 (cosθ + sinθ) and 3k = 4 + 5 (sinθ - cosθ) If H (α, β) is the orthocnetre then OG : GH = 1 : 2 ⇒ α = 3h , β = 3k ⇒ cosθ + sinθ =
α−3
5
, sinθ - cosθ =
β−4
5
⇒ sinθ =
α+β−7
10
, cosθ =
α−β+1
10
Thus, the locus of (α , β) is (x+y−7)2 + (x−y+1)2 = 100