Q.

The area of trapezium whose vertices lie on parabola y2=4x and its diagonals pass through (1,. 0) and having length 254 units each, is

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a

25

b

754

c

75

d

254

answer is D.

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Detailed Solution

Given parabola y2=4x a=1

Diagonals are Intersect at focus    

Question Image

 AC, BD are focal chords.

A=at2, 2at=t2, 2t B=t2, -2t C=at2, -2at=1t2, -2t, D=1t2, 2t

Length of diagonal AC=t+1t2

                         t+1t2=254  t+1t=52  t=  2 (or) 12

A=(4, 4), B(4, -4), C14, -1, D14, 1 AB=8,  CD=2 distance between AB and CD=154 Now Area=12AB+CD (distance between AB and CD)          =12 10 154=754

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The area of trapezium whose vertices lie on parabola y2=4x and its diagonals pass through (1,. 0) and having length 254 units each, is