Q25 of 26 Page 1

Prove that the curves and divide the area of square bounded by and into three equal parts.

Given: curves are y2 = 4x and x2 = 4y


Let three areas divided by curves be A1, A2, A3


A1, A2, A3 denote areas OSPQO, OSPTO and OTPRO respectively


To prove: the given curves divide the area of square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts i.e. A1= A2= A3





Now,















Now,








This shows that the given curves divide the area of square bounded by x = 0, x = 4, y = 4 and y = 0 into three equal parts.


Hence Proved


More from this chapter

All 26 →
22

Find the position vector of the foot of perpendicular and the perpendicular distance from the point P with position vector to the plane Also find image of P in the plane.

 23

Show that the binary operation * on defined as for all is commutative and associative on A. Also find the identify element of * in A and prove that every element of A is invertible.

 24

Prove that the least perimeter of an isosceles triangle in which a circle of radius r can be inscribed is

26

Using properties of determinants, show that is triangle ABC is isosceles if:


OR


A shopkeeper has 3 varieties of pens ‘A’, ‘B’ and ‘C’. Meenu purchased 1 pen of each variety for a total of ₹ 21. Jeevan purchased 4 pens of ‘A’ variety, 3 pens of ‘B’ variety and 2 pens of ‘C’ variety for ₹ 60. While Shikha purchased 6 pens of ‘A’ variety, 2 pens of ‘B’ variety and 3 pens of ‘C’ variety for ₹ 70. Using matrix method, find cost of each variety of pen.