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 25 4 and it passes through the point (1, 0), then the area of ABCD is
Step-by-Step Solution
Key Concept: Apply the core result for parabola parameters and tangents and simplify using the given constraints.
(1) a 2a 2 A (at , 2at) &C ( ,- ) 1 2 t t1 1 2 1 25 1 5 Length AC = a(t1 + ) = , t1 + = $\pm$ t1 4 t1 2 1 1 1 \Rightarrow t1 = 2 or , A( , 1) , D ( , -1) , B(4, 4), C(4, -4) 2 2 4 So, area of trapezium = 1 2 (8 + 2) (4 - 1 4 ) = 75 4
Correct Answer: 1