2D Geometry QA 5
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The document discusses a problem regarding an ellipse inscribed in a rectangle and another ellipse that circumscribes the same rectangle, specifically detailing their equations and properties. It includes the derivation of the rectangle's sides, vertices, and eccentricity of the ellipses involved. The final conclusion indicates the correct option for the eccentricity is (c) based on the calculations provided.
2D Geometry QA 5
- 1. Physics Helpline L K Satapathy JEE Question on Ellipse 2D Geometry QA 5
- 2. Physics Helpline L K Satapathy 2D Geometry QA 5 Question : The ellipse is inscribed in a rectangle R whose sides are parallel to the coordinate axes. Another ellipse , passing through the point (0,4) circumscribes the rectangle R . Then the eccentricity of the ellipse is 22 1 : 1 9 4 yxE 2E 2E 31 1 3( ) ( ) ( ) ( ) 2 2 42 a b c d Answer : Ellipse is bounded by the lines x = 3 and y = 2 Equations of sides of rectangle ABCD are x = 3 and y = 2 Vertices are A (– 3 , 2 ) B ( 3 , 2) C ( 3 , – 2 ) D ( – 3 , – 2 ) Equation of given ellipse : 22 1 . . . (1) 9 4 yx A D B C x y O 2E 1E 2 2 9 4a and b
- 3. Physics Helpline L K Satapathy 2D Geometry QA 5 2 2 2 9 4 9 3(3,2) (3) 1 12 16 4 B a a a 2 2 2 16 12 4c a b 2 1 4 2 ce a 22 1 12 16 yx 2 2 16 , 12a b Correct option = (c) 2 2 2 2 0 16(0,4) 1 16E b a b Let the equation of ellipse E2 be 22 2 2 1 . . . (2) yx a b 22 2 (2) 1 . . . (3) 9 yx a The equation of ellipse E2 is
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