Ex 10.2, 13 - Line through (2, 2) and cutting off intercepts  - Ex 10.2

  1. Chapter 10 Class 11 Straight Lines
  2. Serial order wise
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Ex 10.2, 13 Find equation of the line passing through the point (2, 2) and cutting off intercepts on the axes whose sum is 9. Equation of the line in intercept form is ๐‘ฅ/๐‘Ž + ๐‘ฆ/๐‘ = 1 where a = x - intercept & b = y-intercept Given that sum of intercepts is 9 a + b = 9 b = 9 โ€“ a Putting value b = 9 โ€“ a in equation ๐‘ฅ/๐‘Ž + ๐‘ฆ/(9 โˆ’ ๐‘Ž) = 1 Since point A(2, 2) lies on the line, it will satisfy the equation of line Putting x = 2 & y = 2 in the equation 2/๐‘Ž + 2/(9 โˆ’ ๐‘Ž) = 1 ((9 โˆ’ a)2 + 2a)/(a(9 โˆ’ a)) = 1 18 โ€“ 2a + 2a = a(9 โ€“ a) 18 โ€“ 0 = 9a โ€“ a2 18 = 9a โ€“ a2 a2 โ€“ 9a + 18 = 0 a2 โ€“ 6a โ€“ 3a + 18 = 0 a(a โ€“ 6) โ€“ 3(a โ€“ 6)= 0 (a โ€“ 3) (a โ€“ 6) = 0 So, a = 3 & a = 6

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