BITSAT Mathematics Question (2021) — Solution

Step-by-step solution

Given circles are x^ 2 +y^ 2 =1 (i) and (x-1)^ 2 +y^ 2 =1 (ii) Centre of (i) is O (0,0) and radius =1 Both these circle are symmetrical about x-axis solving (i) and (ii), we get, -2 x+1=0 x= 1 2 array l then y^ 2 =1- ( 1 2 )^ 2 =34 \\ y= 3 2 array The points of intersection are P ( 1 2 , 3 2 ) and Q ( 1 2 ,- 3 2 ) It is clear from the figure that the shaded portion in region whose area is required. Required area = area OQAPO =2 area of the region OLAP =2 ( area of the region O L P O+ area of L A P L ) =2 [ _ 0 ^ 1 2 1-(x-1)^ 2 d x+ _ 1 2 ^ 1 1-x^ 2 dx ] =2 [ (x-1) 1-(x-1)^ 2 2 + 1 2 ^ -1 (x-1) ]_ 0 ^ 1 2 +2 [ x 1-x^ 2 2 + 1 2 ^ -1 x ]_ 1 2 ^ 1 =- 1 2 3 2 + ^ -1 ( -1 2 )- ^ -1 (-1)+0+ ^ -1 (1)- ( 1 2 3 2 + ^ -1 ( 1 2 ) ) = ( 2 3 - 3 2 ) sq. units.