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AP EAMCET · Maths · Hyperbola

If a hyperbola has asymptotes \(3 x-4 y-1=0\) and \(4 x-3 y-6=0\), then the transverse and conjugate axes of that hyperbola are

  1. A \(x+y-5=0, x-y-1=0\)
  2. B \(4 x-3 y=0,3 x+4 y=0\)
  3. C \(3 x-4 y=0,4 x+3 y=0\)
  4. D \(x+2 y-1=0,2 x-y+1=0\)
Verified Solution

Answer & Solution

Correct Answer

(A) \(x+y-5=0, x-y-1=0\)

Step-by-step Solution

Detailed explanation

\(\frac{3x - 4y - 1}{\sqrt{3^2 + (-4)^2}} = \pm \frac{4x - 3y - 6}{\sqrt{4^2 + (-3)^2}}\) \(\frac{3x - 4y - 1}{5} = \pm \frac{4x - 3y - 6}{5}\) \(3x - 4y - 1 = 4x - 3y - 6 \implies x + y - 5 = 0\) \(3x - 4y - 1 = -(4x - 3y - 6) \implies 7x - 7y - 7 = 0 \implies x - y - 1 = 0\)…