Question

A(1, 0) and B(0, 1) are two fixed points on the circle $x^2+y^2=1$. C is a variable point of this circle. As C moves, the locus of orthocenter of the triangle ABC is

• A. $x^2+y^2–2x–2y+1=0$
• B. $x^2+y^2–x–y=0$
• C. $x^2+y^2=4$
• D. $x^2+y^2+2x–2y+1=0$

Answer 1

The correct option is A

$x^2+y^2–2x–2y+1=0$

Centroid divide the line joining orthocenter and circumcentre in 2 : 1

$\Rightarrow h=1+cos\theta ,k=1+sin\theta \Rightarrow (x–1{)}^2+(y–1{)}^2=1$