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All chords of the curve 3x 2 – y 2 – 2x + 4y = 0 that subtends a right angle at the origin, pass through a fixed point whose co-ordinate is Options (1, - 2) (1, 2) (- 1, 2) (- 1, - 2)

All chords of the curve 3x2 – y2 – 2x + 4y = 0 that subtends a right angle at the origin, pass through a fixed point whose co-ordinate is

Options

(1, - 2)
(1, 2)
(- 1, 2)
(- 1, - 2)

Grade:

1 Answers

Vikas TU
14149 Points
3 years ago
 let the chord be y = mx+c
 
therefore,  1=(y-mx)/c
 
substituting in the curve eq. :  (3x^2-y^2) - (2x-4y)(1)=0
  (3x^2-y^2) - (2x-4y)((y-mx)/c)=0
  now simply solve the eq... u will get the followin result:
  (3c+2m)x2 + (4m-2)xy +(-c-4)y2 =0
 
 
these lines are perpendicular
so a+b =0
  3c +2m -c-4 =0
2=m*1 +c 
compair this with the chord y=mx +c
so it will always pass throug
 (1,2)

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