Let x 2 a 2 + y 2 b 2 = 1 a > b be a given ellipse, length of whose latus rectum is 10 . If its eccentricity is the maximum value of the function, ϕ t = 5 12 + t - t 2 , then a 2 + b 2 is equal to :

Question

Let x 2 a 2 + y 2 b 2 = 1 a &#62; b be a given ellipse, length of whose latus rectum is 10 . If its eccentricity is the maximum value of the function, &#981; t = 5 12 + t - t 2 , then a 2 + b 2 is equal to :

Aicharya · Accepted Answer

L R = 2 b 2 a = 10 &#8658; &#8201;&#8201;&#8201; b 2 = 5 a &#981; t = 5 12 &#8722; t 2 - t + 1 4 &#8722; 1 4 = 5 12 + 1 4 &#8722; t &#8722; 1 2 2 = 2 3 &#8722; t &#8722; 1 2 2 max &#981; t = 2 3 = e b 2 = a 2 1 &#8722; e 2 5 a = a 2 1 &#8722; 4 9 &#8658; &#8201;&#8201; 5 = 5 9 a &#8658; &#8201;&#8201;&#8201; a 2 = 81 , &#8201;&#8201; b 2 = 45 a 2 + b 2 = 126 .

Let x 2 a 2 + y 2 b 2 = 1 a > b be a given ellipse, length of whose latus rectum is 10 . If its…

Solution

Let x 2 a 2 + y 2 b 2 = 1 a &#62; b be a given ellipse, length of whose latus rectum is 10 . If its…

Solution

Let x 2 a 2 + y 2 b 2 = 1 a > b be a given ellipse, length of whose latus rectum is 10 . If its…