Let θ be the acute angle between the tangents to the ellipse x 2 9 + y 2 1 = 1 and the circle x 2 + y 2 = 3 at their point of intersection in the first quadrant. Then tan θ is equal to :

Step-by-step solution

Given, x 2 9 + y 2 1 = 1       . . . 1 x 2 + y 2 = 3       . . . 2 On solving equations 1   &   2 , we get x 2 9 + 3 - x 2 1 = 1 ⇒ x 2 + 27 - 9 x 2 = 9 ⇒ 8 x 2 = 18 ⇒ x 2 = 9 4 ⇒ x = ± 3 2 ⇒ x = 3 2 Since, point of intersection in the first quadrant. Put, x = 3 2 in equation 2 , we get y = 3 2 . Hence, the point of intersection of the curves x 2 9 + y 2 1 = 1 and x 2 + y 2 = 3 in the first quadrant is 3 2 ,   3 2 Now, differentiate