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Ex 8.2, 6 - Smaller area enclosed by circle x2 + y2 = 4, line - Ex 8.2

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  1. Chapter 8 Class 12 Application of Integrals
  2. Serial order wise
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Ex 8.2 , 6 Smaller area enclosed by the circle ๐‘ฅ2+๐‘ฆ2 =4 and the line ๐‘ฅ+๐‘ฆ=2 is (A) 2 (ฯ€ โ€“ 2) (B) ฯ€ โ€“ 2 (C) 2ฯ€ โ€“ 1 (D) 2 (ฯ€ + 2) Step 1: Drawing figure Circle is ๐‘ฅ2+๐‘ฆ2 =4 (๐‘ฅโˆ’0)2+(๐‘ฆโˆ’0)2 = 2๏ทฎ2๏ทฏ So, Center = (0, 0) & Radius = 2 Also, ๐‘ฅ+๐‘ฆ=2 passes through (0, 2) & (2, 0) Hence, intersecting points A = (2, 0) & B = (0, 2) Thus, Area required = Area OACB โˆ’ AREA OAB = ๐œ‹ โˆ’ 2 Thus, Option (B) is correct.

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