Vertices of a variable triangle are A`(3,4),B(5costheta, 5sintheta)` and C`(5sintheta,-5costheta)` where `theta` is a parameter then, find the locus of its orthocentre.

Answer

A

Explanation

Let the vertices be `O(0,0),A(alpha,0)`, and `B(alpha_1,beta_1)`, where `0le alphale1 ` and `1lealpha_(1)^(2)+beta_(1)^(2) le4`
So, the area of `DeltaOAB` is maximum where `alpha=1` and `(alpha_1,beta_1)` is (2,0)
In this case, `a=1,b=2`, and `c=sqrt5`,which satisfies `2lecle3`. Therefore, the maximum area is 1.