Last Updated On [03-11-2023]
Rectangle 
has area 200. An ellipse with area 
passes through 
and 
and has foci at 
and 
. If the perimeter of the rectangle is 
, then the value of 
is
Rectangle has area 200. An ellipse with area passes through and and has foci at and . If the perimeter of the rectangle is , then the value of is
Question ID - 153553 :-
Rectangle has area 200. An ellipse with area passes through and and has foci at and . If the perimeter of the rectangle is , then the value of is
|
Rectangle |
(4)
Let sides of rectangle be 
and 
Area of rectangle
(1)
.png)
Area of ellipse 
(2)
We have to find the perimeter of rectangle 
From triangle 
Distance 
distance between foci
or 
or 
(3)
Also from the definition of ellipse sum of focal length is 
,
Then 
(4)
Putting value of 
in equation (3) and (4)
We have 
(using equation (1))
From equation (2), 
Since 
(from equation (4))
Therefore perimeter 
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