Question

A particle moves in xy plane according to the law x = a sin ωt and y = a(1 - cos ωt), where a and w are constant. The particle traces

• A. (A) a straight line equally inclined to x-axis and y-axis
• B. (B) a parabola
• C. (C) a circle
• D. (D) None of these

Answer 1

Answer: (C)

(C) a circle

Answer 2

Explanation:
x=asin⁡ωt…(i)y=a(1−cos⁡ωt)…(ii)x2=a2sin2⁡ωt=a2(1−cos2⁡ωt)x2=a2−a2cos2⁡ωta2cos2⁡ωt=a2−x2y=a(1−cos⁡ωt)=a−acos⁡ωta−y=acos⁡ωt(a−y)2=(acos⁡ωt)2a2+y2−2ay=a2cos2⁡ωt…(iv)Put the value from equation (iii), a2+y2−2ay=a2−x2x2+y2−2ay=0This is the equation of a circle.