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AP EAMCET2011MathematicsStraight Lines

If s and p are respectively the sum and the product of the slopes of the lines 3 x^2-2 x y-15 y^2=0 , then s: p is equal to

Options

  1. A4 : 3
  2. B2 : 3
  3. C3 : 5
  4. D3 : 4

Correct answer

B. 2 : 3

Step-by-step solution

Given pair of lines is 3 x^2-2 x y-15 y^2=0 on compare with, aligned & a x^2+2 h x y+b y^2=0 & a=3, h=-1, b=-15 aligned Now, sum of slopes, s=m₁+m₂= -2 h b = -2(-1) -15 = -2 15 and product of slopes p=m₁ m₂= a b = 3 -15 = -3 15 Then, s: p= -2 15 : -3 15 =2: 3

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