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AP EAMCET202318 May 2023Evening ShiftMathematicsHyperbolaActual

Let X - axis be the transverse axis and Y -axis be the conjugate axis of a hyperbola H . Let x ^2+ y ^2=16 be the director circle of H . If the perpendicular distance from the centre of H to its latus rectum is 34 then a + b =

Options

  1. A8
  2. B9
  3. C5
  4. D7

Correct answer

A. 8

Step-by-step solution

We have equation of the director circle of hyperbola aligned & x^2 a^2 - y^2 b^2 =1 is x^2+y^2=a^2-b^2 & a^2-b^2=16 aligned We have the perpendicular distance from centre (0,0) of hyperbola to its latus rectum is ae. aligned & ae = c = 34 c ^2=34 & b ^2+ a ^2= c ^2=34 aligned solving equations (i) and (ii) we get a=5 & b=3 a+b=5+3=8 .

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