Find the equation of the normal to the curve `3x^2-y^2=8` which are parallel to the line `x+3y-5=0`

Explanation

To find the equation of the normal to the curve \(3x^2 - y^2 = 8\) that is parallel to the line \(x + 3y - 5 = 0\), we will follow these steps:

### Step 1: Find the slope of the given line
The equation of the line is given as \(x + 3y - 5 = 0\). We can rearrange this into slope-intercept form \(y = mx + c\) to find the slope.

\[ 3y = -x + 5 \implies y = -\frac{1}{3}x + \frac{5}{3} \]
...