Q. 265.0( 1 Vote )

Find the area of the region bounded by the parabola y2 = 2x + 1 and the line x – y – 1 = 0.

Answer :

To find area bounded by

y2 = 2x + 1 ...(i)


X – y – 1 = 0. ...(ii)


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


X – y = 1


Or y2 = 2(y – 1) + 1


Or y2 = 2y – 1


Or (y + 1)(y – 3) = 0


Or y = 3 or – 1


x = 4,0


Equation (i) is a parabola with vertex and passes through (0, 1), A (0, – 1)


Equation (ii) is a line passing through (1, 0) and (0, – 1).


Points of intersection of parabola and line are B (4, 3) and A (0, – 1)


These are shown in the graph below: -



Required area = Region ABCDA









Area of the region bounded by the parabola y2 = 2x + 1 and the line x – y – 1 = 0is .


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