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

circle

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Solution

The correct option is A circle
Let $c = (cos θ, sin θ)$
$H = (h, k)$ be orthocenter of $△ A B C$
$h = 1 + cos θ$
$k = 1 + sin θ$
$(x - 1)^{2} + (y - 1)^{2} = 1$
$= x^{2} + y^{2} - 2 x - 2 y + 1 = 0$

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A(1,0) and B(0,1) and two fixed points on the circle x2+y2=1. C is a variable point on this circle. As C moves, the locus of the orthocentre of the triangle ABC is?

The correct option is A circleLet c=(cosθ,sinθ)H=(h,k) be orthocenter of △ABCh=1+cosθk=1+sinθ(x−1)2+(y−1)2=1=x2+y2−2x−2y+1=0

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

The correct option is A circle
Let $c = (cos θ, sin θ)$
$H = (h, k)$ be orthocenter of $△ A B C$
$h = 1 + cos θ$
$k = 1 + sin θ$
$(x - 1)^{2} + (y - 1)^{2} = 1$
$= x^{2} + y^{2} - 2 x - 2 y + 1 = 0$