A stick of length r units slides with its ends on coordinate axes. Then the locus of the midpoint of the stick is a curve whose length is

Step-by-step solution

Let the stick intercepts x -axis at point a , 0 and y -axis at point 0 , b and α , β are midpoints of the stick. then, a + 0 2 = α ⇒ a = 2 α b + 0 2 = β ⇒ b = 2 β Now given length of stick is r units, Then, r 2 = a - 0 2 + 0 - b 2 ⇒ r 2 = a 2 + b 2 ⇒ r 2 = 2 α 2 + 2 β 2 ⇒ r 2 = 4 α 2 + 4 β 2 α 2 + β 2 = r 2 2 If we replace α , β by x , y then, our equation becomes, x 2 + y 2 = r 2 2 So, locus will be a circle with ce