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Let the hyperbola H : 1 b y a x 2 2 2 2 = − pass through the point ( 2 2 , – 2 2 ). A parabola is drawn whose focus is same as the focus of H with positive abscissa and the directrix of the parabola passes through the other focus of H. If the length of the latus rectum of the parabola is e times the length of the latus rectum of H, where e is the eccentricity of H, then which of the following points lies on the parabola ?

1. ) 2 3 , 3 2 (
2. ) 2 6 , 3 3 ( −
3. ) 6 , 3 ( −
4. ) 2 6 , 6 3 (

Correct answer: ) 2 6 , 3 3 ( −

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