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 = 0
is 
.
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