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AP EAMCET201920 Apr 2019Morning ShiftMathematicsHyperbolaActual

The equation of a tangent to the hyperbola (16 x^2-25 y^2-96 x+100 y-356=0 ) which makes an angle (45^ ) with its transverse axis is

Options

  1. A(x-y+2=0 )
  2. B(x-y+4=0 )
  3. C(x+y+2=0 )
  4. D(x+y+4=0 )

Correct answer

A. (x-y+2=0 )

Step-by-step solution

Given equation of hyperbola ( aligned & 16 x^2-25 y^2-96 x+100 y-356=0 & (x-3)^2 25 - (y-2)^2 16 =1 (i) aligned ) Now equation of tangent to the hyperbola (i) having slope ' 1 ' is ( aligned y-2 & =1(x-3)+ 25(1)-16 y-2 & =x-3+3 y-2 & =x-3+3 or y-2=x-3-3 or x-y-4 & =0 x-y+2 & =0 aligned ) Hence, option (1) is correct.

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