Solve this:
Area of the trapezium whose vertices lie on the parabola y2 = 4x and its diagonals pass through (1, 0) and having length 25 4 unit each, is
A) 75 4 sq. unit            B) 625 16 sq. unit           C) 25 4 sq. unit             D) 25 8 sq. unit

Dear student,
Here is the solution of your asked query:
Let A,B,C and D are vertices of trapezium.Focus of the parabola y2=4x is (1,0)So diagonals are focal chordAS=1+t2=m (Let)1m+1254-m=1   {since 1AS+1CS=1a}254=254m-m24m2-25m+25=0m=54 or 5For m=54 1+t2=54 t2=54-1=14t=±12For m=51+t2=5t2=5-1=4t=±2So, coordinates of A, B, C and D are A 14,1; B 4,4, C4,-4 and D 14,-1AD=2 and BC=8So, distance between AD and BC = 154So, area of trapezium ABCD = 122+8×154=754 sq. units.
Regards

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