<s>[INST] Equation of circle after rolling Q: A circle of radius $5$ units touches both the axes and lies in the first quadrant. If the circle makes one complete roll on $+ x$-axis, then what will be its equation in the new position $?$
I got my answer as $x^2 +y^2 -x(10+20\pi)-10y+100\pi^2+100\pi+25=0.$
Is it correct?  
 [/INST] The circle travels a distance of $2\pi\cdot 5=10\pi$ units to the right after one full rotation. It's original equation is $(x-5)^2+(y-5)^2=5^2$. Hence, its new position is
$$(x-5-10\pi)^2+(y-5)^2=5^2\iff (x-5(1+2\pi))^2+(y-5)^2=25\\\iff x^2-10(1+2\pi)x+25(1+2\pi)^2+y^2-10y+25=25\\\iff x^2+y^2-x(10+20\pi)-10y+100\pi^2+100\pi+25=0$$
So yes, you're correct.
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