The slopes of the common tangents of the hyperbolas `(x^(2))/(9)-(y^(2))/(16)=1` and `(y^(2))/(9)-(x^(2))/(16)=1`, are

Options

A. `+-2`
B. `+-1`
C. `+-1//2`
D. none of these

Explanation

To find the slopes of the common tangents of the hyperbolas given by the equations \(\frac{x^2}{9} - \frac{y^2}{16} = 1\) and \(\frac{y^2}{9} - \frac{x^2}{16} = 1\), we can follow these steps:

### Step 1: Identify the parameters of the hyperbolas
For the first hyperbola \(\frac{x^2}{9} - \frac{y^2}{16} = 1\):
- \(a^2 = 9\) (thus \(a = 3\))
- \(b^2 = 16\) (thus \(b = 4\))

For the second hyperbola \(\frac{y^2}{9} - \frac{x^2}{16} = 1\):
...