If y=mx+c is tangent to the hyperbola x2a2−y2b2=1having eccentricity 5, then the least positive integral value of m is

If $y = mx + c$ is tangent to the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ having eccentricity 5, then the least positive integral value of m is

$e^{2} = \frac{b^{2}}{a^{2}} + 1 \Rightarrow \frac{b^{2}}{a^{2}} = 24$

Condition of tangency is $c^{2} = a^{2} m^{2} - b^{2} \geq 0 \Rightarrow m^{2} \geq \frac{b^{2}}{a^{2}}$

$\Rightarrow$ $m \geq 2 \sqrt{6}$

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