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  • A circle of radius 5 units touches both the axes and lies in first quadrant. If the circle makes one complete roll on x-axis along the positive direction of x-axis, then

A circle of radius 5 units touches both the axes and lies in first quadrant. If the circle makes one complete roll on x-axis along the positive direction of x-axis, then its equation in the new position is 

 

Option: 1

x^2+y^2+20 \pi x-10 y+100 \pi^2=0


Option: 2

x^2+y^2+20 \pi x+10 y+100 \pi^2=0


Option: 3

x^2+y^2-20 \pi x-10 y+100 \pi^2=0


Option: 4

\mathrm{None \, \, of \, \, these}


Answers (1)

best_answer

The x-coordinate of the new position of the circle is 5+ circumferrence of the first circle =5+10 \pi

The y-coordinate is 5 and the radius is also 5.

Hence, the equation of the circle in the new position is (x-5-10 \pi)^2+(y-5)^2=(5)^2

\Rightarrow x^2+25+100 \pi^2-10 x+100 \pi-20 \pi x+y^2+25-10 y=25

\Rightarrow x^2+y^2-20 \pi x-10 x-10 y+100 \pi^2+100 \pi+25=0

Posted by

Riya

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