The vertices of a variable triangle are 3,4, 5cosθ,5sinθ, and 5cosθ,−5sinθ, where θ∈R. The locus of its orthocenter is

Distance of all the points from (0,0) are 8 units. The means the circumcenter of the triangle formed by the given points is (0,0) . If G≡h,k is the centroid of the triangle, then 3h=3+5cosθ+sinθ. 3k=4+5sinθ−cosθ. If Hα,β is the orthocente, then OG:GH=1:2 or α=3h, β=3kcosθ+sinθ=α−35.sinθ−cosθ=β−45or sinθ=α+β−710,cosθ=α−β+110Thus, the locus of α,β is x+y−72+x−y+12=100