Let (x1,y1) be one of the points of contact. Given curve is y = cos x ⇒ d
y
dx
= - sin x
dy
dx
|(x1,y1) = - sin x1 Now the equation of the tangent at (x1,y1) is y - y1(
dy
dx
)(x1,y1)(x−x1) ⇒ y−y1 = - sin x1 (0 - x1) ⇒ y1 = −x1sinx1 ... (i) Also, point (x1,y1) lies on y = cos x. ∴ y1 = cos x1 From Eqs. (i), (ii) , we get sin2x1+cos2x1 =
y12
x12
+y12 = 1 ⇒ x12 = y12+y12x12 Hence, the locus of (x1,y1) is x2 = y2+y2x2 ⇒ x2y2 = x2−y2