If the minimum area of the triangle formed by a tangent to the ellipse x 2 b 2 + y 2 4 a 2 = 1 and the co-ordinate axis is k a b , then k is equal to ___________.

Step-by-step solution

Equation of tangent at parametric point b   cos θ , 2 a   sin   θ   to the ellipse is x b cos   θ + y 2 a sin   θ = 1 Co-ordinates of P b cos   θ , 0 and Q 0 , 2 a sin   θ respectively. Therefore, Area of triangle formed by tangent and co-ordinate axes = 1 2 × b cos   θ × 2 a sin   θ = a b sin   θ . cos   θ = 2 a b sin   2 θ as sin   θ ≤ 1 therefore we can say Minimum are