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COMEDK2014MathematicsStraight Lines

If a is a parameter then an equation of a family of lines having the sum of the intercepts on axes equal to 7 is

Options

  1. A4 x+3 y=12 a
  2. B3 x+4 y=7 a
  3. C7 x+a y=a(7-a)
  4. Da y=(7-a)(a-x)

Correct answer

D. a y=(7-a)(a-x)

Step-by-step solution

Since, equation of family of lines is x a + y b =1 (i) Sum of intercepts =a+b=7 (given) b=7-a Substitute b=7-a in Eq. (i), we get gathered x a + y 7-a =1 (7-a) x+a y=a(7-a) a y=(7-a)(a-x) gathered

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