The point on the ellipse x 2 6 + y 2 3 = 1 which is nearest to the line x + y = 7 is

Step-by-step solution

Shortest distance always lies along the common normal ⇒ Slope of common normal is 1 Now, the equation of the normal at the point acos ⁡ θ , bsin ⁡ θ   on   x 2 a 2 + y 2 b 2 = 1 is a x c o s θ - b y s i n θ = a 2 - b 2 , where slope is a b tan ⁡ θ ⇒ 6 3 tan ⁡ θ = 1 ⇒ tan ⁡ θ = 1 2 ⇒ sin ⁡ θ = 1 3 and cos ⁡ θ = 2 3 or sin ⁡ θ = - 1 3 ,   cos ⁡ θ = - 2 3 (rejected because