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  • The distance between two parallel tangents drawn to the hyperbola <img alt="\mathrm{\frac{x^2}{9}-\frac{y^2}{49}=1}" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%5Cfrac%7B

The distance between two parallel tangents drawn to the hyperbola \mathrm{\frac{x^2}{9}-\frac{y^2}{49}=1} is 2 , then their slope is equal to m. The value of \mathrm{|2 m|} is equal to ____________.

Option: 1

1


Option: 2

3


Option: 3

5


Option: 4

8


Answers (1)

According to the question,

\mathrm{ \begin{aligned} & \frac{2 \sqrt{9 m^2-49}}{\sqrt{1+m^2}}=2 \\\\ & \text { or } 9 m^2-49=1+m^2 \\\\ & \text { or } 8 m^2=50 \\\\ & \text { or } m= \pm \frac{5}{2},|2 m|=5 \end{aligned} }

Posted by

Ramraj Saini

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