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The area of the region enclosed by the parabola (y-2)2=x-1, the line x-2 y+4=0 and the positive coordinate axes is .
5
x=2y-4 in (y-2)2=x-1 (y-3)2=0 the line touches the parabola at (2, 3)
[figure]
Area (horizontal strips) = 03 [(y-2)2+1 ]dy- 23(2y-4) dy
= [ (y-2)33+y ]03- [y2-4y ]23
= ( 13+3+ 83 )-(-3+4)=6-1=5
Answer: 5
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