Find the equations of the tangent and normal to the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1`. at the point `(x_0,y_0)`

Explanation

To find the equations of the tangent and normal to the hyperbola \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\) at the point \((x_0, y_0)\), we can follow these steps:

### Step 1: Differentiate the Hyperbola
We start with the equation of the hyperbola:
\[ \frac{x^2}{a^2} - \frac{y^2}{b^2} = 1 \]
Differentiating both sides with respect to \(x\):
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