51.Find the area of the region enclosed between the two circles x2 + y2 = 4 and (x - 2)2 + y2 = 4.
The equations of the given circles are               and          ...(2)  Equation (1) is a circle with centre O at the origin and radius 2. Equation (2) is a circle with centre C(2, 0) and radius 2.   Solving equations (1) and (2), we have              or          or          or            x = 1   from  (1),   Â
 the points of intersection of the given circles are Required area of the enclosed region OACA'O between the circles    = 2 [area of region ODCAO]    =2 [area of region ODAO + area of the region DCAD]                                          Â
    Â
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52.Find the area of the region enclosed between the two circles  x2 + y2 = 1 and (x - 1)2 + y2 = 1.Â
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53.Find the area of the region enclosed between the two circles x2Â + y2Â = 1 andÂ
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Short Answer Type
54.Find the area of the region bounded by two parabola 4 y = x2 and 4 x = y2
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Long Answer Type
55.Find the area included between the two curves y2Â = 9x and ,x2Â = 9y. Also draw the rough sketch.
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Short Answer Type
56.
Calculate the area of the region bounded by the y = x2 and x = y2.
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Long Answer Type
57.Draw a graph of y2Â = 16 x and x2Â = 16y, and evaluate the area between them.
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58.Find the area of the region included between the parabolas y2Â = 4 a x and x2Â = 4 a y, a > 0. Â Â
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59.Draw the rough sketch of y2Â = x + 1 and y2Â = - x + 1 and determine the area enclosed by the two curves.
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60.Find the area of the region {(x, y): 0 ≤ y ≤ x2 + 1 , 0 ≤ y ≤ x + 1, 0 ≤ x ≤ 2}.
Long Answer Type
 ...(2)
  from  (1),    
 the points of intersection of the given circles are 
Short Answer Type
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