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AP EAMCET2004MathematicsStraight Lines

If the distance between the points (a , a ) and (a , a ) is 2 a , then is equal to

Options

  1. A2 n + , n Z
  2. Bn + 2 + , n Z
  3. Cn - , n Z
  4. D2 n + , n Z

Correct answer

A. 2 n + , n Z

Step-by-step solution

Let the points be A=(a , a ) and aligned & B=(a , a ) & A B= (a -a )^2 +(a -a )^2 & = a^2 ^2 +a^2 ^2 -2 a^2 & +a^2 ^2 +a^2 ^2 -2 a^2 aligned aligned & = 2 a^2-2 a^2( + ) & = 2 a( 1- ( - ) & 2 a= 2 a 2 ( - 2 ) & ( - 2 )=1 - 2 =n 2 & ( - 2 )=1 - 2 =n 2 & - =2 n & =2 n + & aligned where, n Z

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