**NCERT Solutions for Maths Class 12 Exercise 8.2**

Hello Students. Welcome to **maths-formula.com**. In this post, you will find the complete** ****NCERT Solutions for Maths Class 12 Exercise 8.2**.

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Class 12th is a very crucial stage of your student’s life, since you take all important decisions about your career on this stage. Mathematics plays a vital role to take decision for your career because if you are good in mathematics, you can choose engineering and technology field as your career.

**NCERT Solutions for Maths Class 12 Exercise 8.2** helps you to solve each and every problem with step by step explanation which makes you strong in mathematics.

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**NCERT Solutions for Maths Class 12 Exercise 8.2** are prepared by the experienced teachers of CBSE board. If you are preparing for JEE Mains and NEET level exams, then it will definitely make your foundation strong.

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**NCERT Solutions for Maths Class 12 Exercise 8.1**

**NCERT Solutions for Maths Class 12 Exercise 8.2**

**Maths Class
12 Ex 8.2 Question 1.**

Find the area of
the circle 4*x*² + 4*y*² = 9 which is interior to the parabola
*x*² = 4*y*.

**Solution:**

The required area
is bounded by the circle 4*x*² + 4*y*² = 9 and interior of the parabola *x*² = 4*y*.

Putting *x*² = 4*y* in *x*² + *y*² = 9/4

We get 4*y* + *y*² = 9/4

**Maths Class
12 Ex 8.2 Question 2.**

Find the area
bounded by curves (*x* – 1)² + *y*² = 1 and *x*² + *y*² = 1.

**Solution:**

The given circles
are *x*² + *y*² = 1 … (i)

and (*x* – 1)² + *y*² = 1 … (ii)

The centre of the circle (i) is O(0, 0) and the radius is 1.

**Maths Class
12 Ex 8.2 Question 3.**

Find the area of
the region bounded by the curves *y* = *x*² + 2, *y* = *x*, *x* = 0 and *x* = 3.

**Solution:**

The equation of
the parabola is *y* = *x*² + 2 or *x*² = *y* – 2

Its vertex is (0, 2) and the axis is *y*-axis.

Boundary lines are *y* = *x*, *x*
= 0 and *x* = 3.

Graphs of the curve and lines have been shown in the following figure.

Area of the region PQRO = Area of the region OAQR – Area of region OAP

**Maths Class
12 Ex 8.2 Question 4.**

Using integration,
find the area of region bounded by the triangle whose vertices are (–1, 0), (1,
3) and (3, 2).

**Solution:**

The points A(–1,
0), B(1, 3) and C(3, 2) are plotted and joined.

Area of ∆ABC = Area of ∆ ABL + Area of trapezium BLMC – Area of ∆ACM … (i)

The equation of the line joining the points

**Maths Class
12 Ex 8.2 Question 5.**

Using integration,
find the area of the triangular region whose sides have the equations *y* = 2*x*
+ 1, *y* = 3*x* + 1 and *x* = 4.

**Solution:**

The given lines
are *y* = 2*x* + 1 … (i)

*y* = 3*x* + 1 … (ii)

and *x* = 4 … (iii)

Subtracting equation (i) from equation (ii), we get *x* = 0.

Putting *x* = 0 in equation (i), we get *y* = 1

∴ Lines (ii) and (i) intersect at A(0, 1)

Putting *x* = 4 in equation (ii), we get *y* = 12 + 1 = 13

∴ Lines (ii) and (iii) intersect at B(4, 13)

Putting *x* = 4 in equation (i), we get *y* = 8 + 1 = 9

∴ Lines (i) and (iii) intersect at C(4,
9)

**Choose the
correct answer in the following exercises 6 and 7.**

**Maths Class
12 Ex 8.2 Question 6.**

Smaller area
bounded by the circle *x*² + *y*² = 4 and the line *x* + *y* = 2 is

(A) 2(Ï€ – 2)

(B) Ï€ – 2

(C) 2Ï€ – 1

(D) 2(Ï€ + 2)

**Solution:**

(B) A circle of
radius 2 and centre at O is drawn. The line AB: *x* + *y* = 2 is passed
through (2, 0) and (0, 2).

Area of the
region ACB = Area of quadrant OAB – Area of ∆OAB … (i)

Hence, the
correct answer is option (B).

**Maths Class
12 Ex 8.2 Question 7.**

Area lying
between the curves *y*² = 4*x* and *y* = 2*x* is

(A) 2/3

(B) 1/3

(C) 1/4

(D) 3/4

**Solution:**

(B) The curve is *y*² = 4*x* … (i)

and the line is *y* = 2*x* … (ii)

Hence, the
correct answer is option (B).