The values of 'm' for which a line with slope m is common tangent to the hyperbola x^ 2…

Mathematics · JEE Main · NTA ExamsCo-ordinate Geometry

The values of 'm' for which a line with slope m is common tangent to the hyperbola \(\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1(a \neq b)\) and parabola \(\scriptstyle\nabla^{2}\;=\;4\mathbf{a}\times\) is
  1. \(m \in[0, \infty)\)
  2. \(m \in(-\infty,-1) \cup(1, \infty)-\left\{ \pm \sqrt{\frac{1+\sqrt{5}}{2}}\right\}\)
  3. \(m \in(-\infty, 2)-\sqrt{\frac{1+\sqrt{5}}{2}}\)
  4. \(m \in(-\infty,-1) \cup(1, \infty)\)

Answer

(B) m (- ,-1) (1, )- 1+ 5 2

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