Q26 of 29 Page 1

Find the area bounded by the curves and x-axis.

OR


Find the area of the region.


The given curves are,



2y+3=x … (2)


Solving (1) and (2) we get,


2y +3 = y2


⇒ y2 – 2y – 3 =0


⇒ y2 – 3y + y – 3 =0


⇒ y(y – 3) + 1(y – 3) = 0


⇒ (y + 1)(y – 3) = 0


⇒ y = –1, 3


As y >0


So, y = 3


Substituting y = 3 in (2) we get,


x = 2(3) + 3


⇒ x = 9


So, (1) and (2) intersect at (9, 3)






= (9+9) – 9 = 9 sq. units


So, required area = 9 sq. units.


OR


The given curves are,


x2 + y2 = 8 … (1)


x2 = 2y … (2)


Solving (1) and (2) we get,


2y + y2 – 8 =


⇒ y2 + 2y – 8 = 0


⇒ y2 + 4y – 2y – 8 = 0


⇒ y(y + 4) – 2(y + 4) = 0


⇒ (y + 4)(y – 2) = 0


⇒ y = – 4, 2


But y > 0 hence, y = 2


Put y = 2 in (2) we get,


x2 = 4


⇒ x = + 2, – 2


So, the point of intersections are (-2, 2) and (2, 2).



So, required area =




As,


So,







Hence,


More from this chapter

All 29 →
24

If findA-1.

Hence, solve the system of equations:


3x + 3y+ 2z = 1


x + 2y = 4


2x – 3y –z = 5


OR


Find the inverse of the following matrix using elementary transformations.


 25

A cuboidal shaped godown with square base is to be constructed. Three times as much cost per square meter is incurred for constructing the roof as compared to the walls. Find the dimensions of the godown if it is to enclose a given volume and minimize the cost of constructing the roof and the walls.

 27

Find the equation of the plane through the line

and parallel to the line


Hence, find the shortest distance between the lines.


OR


Show that the line of intersection of the planes x+2y+3z=8 and 2x+3y+4z=11 is coplanar with the line


Also, find the equation of the plane containing them.

 28

A manufacturer makes two types of toys A and B. Three machine are needed for this purpose and the time (in minutes) required for each toy on the machines is given below:


The machines I, II and III are available for a maximum of 3 hours, 2 hours and 2 hours 30 minutes respectively. The profit on each toy of type A is Rs 50, and that of type B is Rs 60. Formulate the above problem as a L.P.P and solve it graphically to maximize profit.