RD Sharma - Mathematics (Volume 2)

Book: RD Sharma - Mathematics (Volume 2)

Chapter: 21. Areas of Bounded Regions

Subject: Maths - Class 12th

Q. No. 26 of Exercise 21.3

Listen NCERT Audio Books to boost your productivity and retention power by 2X.

26

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

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 .


Chapter Exercises

More Exercise Questions