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The mid point of the chord 4 x-3 y=5 of the hyperbola 2 x^2-3 y^2=12 is

Options

  1. A(0,- 5 3 )
  2. B(2,1)
  3. C( 5 4 , 0 )
  4. D( 11 4 , 2 )

Correct answer

B. (2,1)

Step-by-step solution

Given, 4 x-3 y=5 and 2 x^2-3 y^2=12 2 ( 5+3 y 4 )^2-3 y^2=12 aligned & (25+9 y^2+30 y ) 8 -3 y^2=12 & 15 y^2-30 y+71=0 & y= 30 900-4260 30 & =1 -3360 30 & aligned Also, aligned & 2 x^2-3 ( 4 x-5 3 )^2=12 & 10 x^2-40 x+61=0 & aligned x= 40 1600-4 10 61 2 10 = 40 -840 20 =2 -840 20 Points are A (2+ -840 20 , 1+ -3360 30 ) and B (2- -840 20 , 1- -3360 30 ) . Mid point of A B is (2,1) .

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