CBSE Class 12-science Answered

let the point of contact is h,k  so line passing through origin is k = mh  ...  (1)having slope  m   point also lie on the curve so k = sinh

slope of tangent of curve y = sin x  is   dy / dx =  cos x    which is equal to m     so m = cos h ...(2)  we have m = k/h from (1)      putting in 2 we get  k/h = cos h  

and we know sin²h + cos² h =1  so locus is k² + (k/h)² = 1 ===> h²k² = h² - k²                                                         which is  x²y² = x² - y²