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AP EAMCET · Maths · Hyperbola

If the equation of the tangent of the hyperbola \(5 x^2-9 y^2-20 x-18 y-34=0\) which makes an angle \(45^{\circ}\) with the positive X -axis in positive direction is \(x+b y+c=0\) then \(b^2+c^2=\)

  1. A 2 or 13
  2. B 5 or 26
  3. C 2 or 26
  4. D 26 or 28
Verified Solution

Answer & Solution

Correct Answer

(C) 2 or 26

Step-by-step Solution

Detailed explanation

\(5(x^2-4x) - 9(y^2+2y) = 34\) \(5(x-2)^2 - 9(y+1)^2 = 34 + 20 - 9 = 45\) \(\frac{(x-2)^2}{9} - \frac{(y+1)^2}{5} = 1\) \(m = \tan(45^{\circ}) = 1\) \((y+1) = 1(x-2) \pm \sqrt{9(1)^2 - 5}\) \(y+1 = x-2 \pm \sqrt{4}\) \(y+1 = x-2 \pm 2\) \(x-y-1=0 \text{ or } x-y-5=0\)…