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Analytical Geometry

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Joined:	5 Oct 2007
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10 Nov 2007 22:14:09 IST

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areas doubt

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the area bounded by the normal at (1,2) to the parabola y^2=4x, y>=0,the itself and the axis of the parabola , is..

options:

1) 2/3 2)4/3 3)8/3 4) 10/3

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nishant singh

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Joined: 23 Feb 2007

Posts: 424

10 Nov 2007 23:05:53 IST

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y^2 = 4x

2y (dy/dx)= 4
dy/dx = 2/y

y=2

dy/dx =1

m-> slope of normal
m(dy/dx)=-1
m=-1
eqution of normal
x-1=-1(y-2)
x+y-3=0

normal meet axis(y=0)
at x=3

now as seen from attached figure
area = _{[0 ]}

^{[1 ]} ydx + area of triangle (1,2),(1,0),(3,0)
= 2_{[0 ]}

^{[1 ]}

x dx + 2
= 2*2/3 *1 +2
= 10/3

answer 10/3

do rate me if understood:)

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