Answer :

To find region bounded by curves

y = x – 1 ...(i)


(y – 1)2 = 4 (x + 1) ...(ii)


On solving the equation (i) and (ii),


Or (x – 1 – 1)2 = 4 (x + 1)


Or (x – 2)2 = 4 (x + 1)


Or x2 + 4 – 4x = 4x + 4


Or x2 – 8x = 0


Or x = 0 or 8


y = – 1 or7


Equation (i) represents a line passing through (1,0) and (0, – 1)


Equation (ii) represents a parabola with vertex ( – 1,1) passes through (0,3),(0, – 1),.


Their points of intersection A(0, – 1) and B(8,7).


These are shown in the graph below: –



It slides from y = – 1 to y = 7,


So, required area = Region ABCDA









The area of the region bounded by the curves y = x – 1 and (y – 1)2 = 4 (x + 1) is


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