Question

A circle of radius $7$ units touches the coordinate axes in the second quadrant. If the circle makes five complete rolls along the positive direction of $x-$axis, then the equation of circle in new position is
$(\text{Assume}\pi =\frac{22}{7})$

• A. $(x+227{)}^2+(y-7{)}^2=49$
• B. $(x-213{)}^2+(y-7{)}^2=49$
• C. $(x-227{)}^2+(y+7{)}^2=49$
• D. $(x+213{)}^2+(y+7{)}^2=49$

Answer 1

The correct option is B $(x-213{)}^2+(y-7{)}^2=49$

Given radius, $r=7$
Centre of the circle in initial position : $C_1\equiv (-7,7)$

When circle rolls five complete cycle along positive direction of $x$-axis, new position of centre is,
$C_2\equiv (-7+5\times 2\pi r,7)$
$\Rightarrow C_2\equiv (-7+5\times 2\times \frac{22}{7}\times 7,7)\equiv (213,7)$
and $r=7$ (fixed)
$\therefore$ Required equation of the circle is
$(x-213{)}^2+(y-7{)}^2=49$