InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
A stick of length `l` slides with its ends on two mutually perpendicular lines. Find the locus of the middle point of the stick. |
|
Answer» Let the stick intercepts x-axis at point `(a,0)` and y-axis at point `(0,b)` and `(alpha, beta)` are midpoints of the stick. then, `(a+0)/2 = alpha => a = 2alpha` `(b+0)/2 = beta=> b= 2beta` Then, `l^2 = (a-0)^2+(0-b)^2` Here, `l` is the length of stick. `=>l^2 = a^2+b^2 ` `=>l^2 = (2alpha)^2+(2beta)^2` `=>l^2 = 4alpha^2+4beta^2` `alpha^2+beta^2 = (l/2)^2` If we replace `(alpha,beta)` by `(x,y)`, then , our equation becomes, `x^2+y^2 = (l/2)^2` So, locus will be a circle with center at origin and radius `l/2`. |
|