The point on the ellipse 16 x 2 + 9 y 2 = 400 , where the ordinate decreases at the same rate at which the abscissa increases is a , b , then a + 3 b can be

Step-by-step solution

Differentiating the equation of ellipse, we get 32 x d x d t + 18 y d y d t = 0 ⇒ 32 x d x d t = - 18 y d y d t As d x d t = - d y d t ∴ 32 x = 18 y ⇒ 16 x = 9 y Putting in the equation of the ellipse, we get, 16 x 2 + 256 81 ⋅ 9 x 2 = 400 ⇒ x 2 + 16 9 x 2 = 25 ⇒ x = ± 3 ⇒ y = ± 16 3 ∴ a = 3 , b = 16 3 ⇒ a + 3 b = 3 + 16 = 19