Let C be the largest circle centred at 2 , 0 and inscribed in the ellipse x 2 36 + y 2 16 = 1 . If 1 , α lies on C , then 10 α 2 is equal to ______

Step-by-step solution

Given: x 2 36 + y 2 16 = 1 Let any point on the ellipse be P 6 cos θ ,   4 sin θ . Equation of normal of ellipse at any point P is 3 sec θ x – 2 cosec θ y = 10 This normal is also the normal of the circle passing through the point 2 , 0 . So, 6 sec θ = 10 or sin θ = 0 (Not possible) cos θ = 3 5 and sin θ = 4 5 So, point P ≡ 18 5 , 16 5 . So, the largest radius of circle r = 320 5 = 64 5 So the equation of circle x - 2 2 + y 2 = 64 5 This circle is passing thr