jee_main_2025_28_jan_morning - Conic Sections Topics

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QUESTION #52 Parabola and Trapezium Properties
Let ABCD be a trapezium whose vertices lie on the parabola y^2 = 4x. Let the sides AD and BC of the trapezium be parallel to y-axis. If the diagonal AC is of length frac254 and it passes through the point (1,0), then the area of ABCD is: (1) frac754 (2) frac252 (3) frac1258 (4) frac758
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QUESTION #75 Infinite Series of Ellipses
Let E_1: fracx^29 + fracy^24 = 1 be an ellipse. Ellipses E_i 's are constructed such that their centres and eccentricities are same as that of E_1 , and the length of minor axis of E_i is the length of major axis of E_i+1 ( i ge 1 ). If A_i is the area of the ellipse E_i , then frac5pi left( sum_i=1^infty A_i right) , is equal to ....
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