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If y=m x+c is tangent to the hyperbola (...

If `y=m x+c` is tangent to the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1,` having eccentricity 5, then the least positive integral value of `m` is_____

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Verified by Experts

The correct Answer is:
5
`e^(2)=(b^(2))/(a^(2))+1or (b^(2))/(a^(2))=e^(2)-1=24`
Now, y = mx + c is tangent to hyperbola
`(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`
Then we must have
`a^(2)m^(2)-b^(2)ge0`
`"or "m^(2)geb^(2)//a^(2)or m^(2)ge24`
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