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 (Assumeπ=227)
A
(x+227)2+(y−7)2=49
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B
(x−213)2+(y−7)2=49
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C
(x−227)2+(y+7)2=49
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D
(x+213)2+(y+7)2=49
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Solution
The correct option is B(x−213)2+(y−7)2=49 Given radius, r=7
Centre of the circle in initial position : C1≡(−7,7)
When circle rolls five complete cycle along positive direction of x-axis, new position of centre is, C2≡(−7+5×2πr,7) ⇒C2≡(−7+5×2×227×7,7)≡(213,7)
and r=7 (fixed) ∴ Required equation of the circle is (x−213)2+(y−7)2=49