The circle $x^{2} - y^{2} - 2 x + 1 = 0$ is method angle the positive direction of $x -$ axis and makes one complete roll. Find its equation in new position.

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Solution

$\begin{matrix} x^{2} - y^{2} - 2 x + 1 = 0 \Rightarrow x^{2} - 2 x + 1 - y^{2} = 0 \Rightarrow {(x - 1)}^{2} + 1 - y^{2} = 1 \Rightarrow {(x - 1)}^{2} + y (1 - y) = 1, r = 1 \end{matrix}$
New equation of circle
$\Rightarrow {x - (1 + 2 π)}^{2} + {(y - 1)}^{2} = 1$

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The circle x2−y2−2x+1=0 is method angle the positive direction of x−axis and makes one complete roll. Find its equation in new position.

x2−y2−2x+1=0⇒x2−2x+1−y2=0⇒(x−1)2+1−y2=1⇒(x−1)2+y(1−y)=1,r=1New equation of circle ⇒{x−(1+2π)}2+(y−1)2=1

The circle $x^{2} - y^{2} - 2 x + 1 = 0$ is method angle the positive direction of $x -$ axis and makes one complete roll. Find its equation in new position.

$\begin{matrix} x^{2} - y^{2} - 2 x + 1 = 0 \Rightarrow x^{2} - 2 x + 1 - y^{2} = 0 \Rightarrow {(x - 1)}^{2} + 1 - y^{2} = 1 \Rightarrow {(x - 1)}^{2} + y (1 - y) = 1, r = 1 \end{matrix}$
New equation of circle
$\Rightarrow {x - (1 + 2 π)}^{2} + {(y - 1)}^{2} = 1$