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The value of $m$ for which $y=m x+6$ is a tangent to the hyperbola $\frac{x^2}{100}-\frac{y^2}{49}=1$, is
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$\sqrt{\frac{17}{20}}$
If $y=m x+c$ touches $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$, then $c^2=a^2 m^2-b^2$. Here $c=6, a^2=100, b^2=49$ $\therefore 36=100 m^2-49 \Rightarrow 100 m^2=85 \Rightarrow m=\sqrt{\frac{17}{20}}$.
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