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AP EAMCET202317 May 2023Morning ShiftMathematicsHyperbolaActual

If P ( 4 ) and Q ( 3 4 ) are two points on the hyperbola 4 x^2-y^2-8 x-2 y-13=0 in parametric form, then the distance between P and Q is

Options

  1. A4 6
  2. B10
  3. C8 3
  4. D5

Correct answer

A. 4 6

Step-by-step solution

aligned & 4 x^2-y^2-8 x-2 y-13=0 & 4(x-1)^2-(y+1)^2=16 & (x-1)^2 4 - (y+1)^2 16 =1 aligned Which can be parametrized as: x=1+2 , y=-1+4 Now, P ( 4 )= (1+2 4 ,-1+4 4 ) gathered P ( 4 )=(1+2 2 , 3) Q ( 3 4 )= (1+2 ( 3 4 ),-1+4 ( 3 4 ) )=(1-2 2 ,-5) gathered Distance between P Q= (1+2 2 -1+2 2 )^2+(-3-5)^2 = 32+64 = 96 =4 6

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