Find the value of m for which `y = mx + 6` is a tangent to the hyperbola `x^2 /100 - y^2 /49 = 1`
Text Solution
AI Generated Solution
To find the value of \( m \) for which the line \( y = mx + 6 \) is a tangent to the hyperbola \( \frac{x^2}{100} - \frac{y^2}{49} = 1 \), we can follow these steps:
### Step 1: Write the equation of the hyperbola and the line
The hyperbola is given by:
\[
\frac{x^2}{100} - \frac{y^2}{49} = 1
\]
The line is given by:
...
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