If point A and B are $\left(1,0\right)$ and $B\left(0,1\right)$ . If point C is on the circle $x^2+y^2=1$ , then locus of the orthocenter of the triangle ABC is

$C\left(\cos \theta ,\sin \theta \right)$ . $H\left(h,k\right)$ is the orthocentre of the $\Delta ABC$

Since circumcentre of the triangle is $\left(0,0\right)$ , for orthocenter $h=1+\cos \theta$ and $k=1+\sin \theta$

Eliminating $\theta$ ,${\left(x-1\right)}^2+{\left(y-1\right)}^2=1$ , hence, $x^2+y^2-2x-2y+1=0$