area of ellipse
suppose semimajor axis of ellipse = a , and semiminor axis = b
The parametric formula of ellipse :
y = b*sin j
x = a*cos j
area of one - quarter of ellipse = INT (0 to a ) y.dx
dx = - a*sin j dj
when x = 0 ..... j = pi/2
when x = a ..... j = 0
area = 4*INT (from j = pi/2 to j = 0) - b*a*sin^2 j .dj
area = 4*INT (from j = 0 to j = pi/2)* a*b (1 - cos 2j)/2 . dj
area = 2*a*b [j - 1/2*sin 2j]from j = 0 to j = pi/2
area = 2*a*b [pi/2 - 0 - 1/2*sin pi + 1/2*sin 0
area = pi*a*b
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hyperbola
Parabola
:
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-
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f-77
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/ hoor_dana
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= 3
:
: ( 0 3 )
1 : ( 6 3 )
2 : ( - 6 3 )
1 : ( 11 3 )
2 : ( - 11 3 )