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

Explanation

To find the value of \( m \) for which the line \( y = mx + 6 \) is tangent to the hyperbola given by \( \frac{x^2}{100} - \frac{y^2}{49} = 1 \), we can follow these steps:

### Step 1: Identify parameters of the hyperbola
The hyperbola is given in the standard form:
\[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \]
From the equation \( \frac{x^2}{100} - \frac{y^2}{49} = 1 \), we can identify:
...