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AP EAMCET202315 May 2023Evening ShiftMathematicsStraight LinesActual

Assertion (A): The difference of the slopes of the lines represented by y ^2-2 xysec ^2 + (3+ ^2 ) (-1+ ^2 ) x ^2=0 is 4 Reason (R): The difference of the slopes represented by a x^2+2 h x y+b y^2=0 is 2 h^2-a b |b|

Options

  1. ABoth A and R are true and R is the correct explanation of A
  2. BBoth A and R are true but R is not correct explanation of A
  3. CA is true but R is false
  4. DA is false but R is true

Correct answer

A. Both A and R are true and R is the correct explanation of A

Step-by-step solution

Since the difference of the slopes of the lines a x^2+2 h x y+b y^2=0 is given by 2 h^2-a b |b| Now the given line is y^2-2 x y ^2 + (3+ ^2 ) (-1+ ^2 ) x^2=0 So the difference of slope is = 2 ( ^2 )^2+ (3+ ^2 ) ( ^2 -1 ) 1 =2 ^2 ( ^2 +3- ^2 ) =2 4 =4 So a is correct option.

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