JEE Advanced Model Paper 4 with solutions for online practice

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