If the line `y=2x+lambda` be a tangent to the hyperbola `36x^(2)-25y^(2)=3600`, then `lambda` is equal to

Options

A. `16`
B. `-16`
C. `+-16`
D. none of these

Explanation

To find the value of \(\lambda\) for the line \(y = 2x + \lambda\) to be a tangent to the hyperbola \(36x^2 - 25y^2 = 3600\), we will follow these steps:

### Step 1: Convert the hyperbola equation to standard form
The given hyperbola equation is:
\[ 36x^2 - 25y^2 = 3600 \]
To convert it to standard form, we divide the entire equation by 3600:
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