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Find the value of m for which y = mx + 6...

Find the value of m for which `y = mx + 6` is a tangent to the hyperbola `x^2 /100 - y^2 /49 = 1`

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If `y=mx+c` touches `(x^(2))/(a^(2))-(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=100m^(2)-49`
`"or "100m^(2)=85`
`"or "m=sqrt((17)/(20))`
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