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WBJEE · Maths · Hyperbola

Equation of a tangent to the hyperbola \(5 x^{2}-y^{2}=5\) and which passes through an external point (2,8) is

  1. A \(3 x-y+2=0\)
  2. B \(3 x+y-14=0\)
  3. C \(23 x-3 y-22=0\)
  4. D \(3 x-23 y+178=0\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(23 x-3 y-22=0\)

Step-by-step Solution

Detailed explanation

Given equation of hyperbola can be write as \(\frac{x^{2}}{1}-\frac{y^{2}}{(\sqrt{5})^{2}}=1\) here, \(a=1\) and \(b=\sqrt{5}\) Since, \(y=m x \pm \sqrt{a^{2} m^{2}-b^{2}}\) \(y=m x \pm \sqrt{m^{2}-5}\) \(\Rightarrow \quad(8-2 m)^{2}=\left(\sqrt{m^{2}-5}\right)^{2}\)…