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  • The value of  for which <img alt="\mathrm{y=mx+6}" src="https://entrancecorner.oncodecogs.co

The value of \mathrm{m} for which \mathrm{y=mx+6} is a tangent to the hyperbola \mathrm{\frac{x^2}{100}-\frac{y^2}{49}=1}, is 

Option: 1

\sqrt{\frac{17}{20}}


Option: 2

\sqrt{\frac{20}{17}}


Option: 3

\sqrt{\frac{3}{20}}


Option: 4

\mathrm{\sqrt{\frac{20}{3}}}


Answers (1)

best_answer

For condition of tangency, \mathrm{c^2=a^2 m^2-b^2 \text {. Here } c=6, a=10, b=7}
Then, \mathrm{(6)^2=(10)^2 \cdot m^2-(7)^2}
\mathrm{36=100 m^2-49 \Rightarrow 100 m^2=85 \Rightarrow m^2=\frac{17}{20} \Rightarrow m=\sqrt{\frac{17}{20}}}

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Gaurav

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