Find the condition for the following set of curves to intersect orthogonally: `(x^2)/(a^2)+(y^2)/(b^2)=1` and `(x^2)/(A^2)-(y^2)/(B^2)=1.`

Explanation

To find the condition for the curves \(\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\) (an ellipse) and \(\frac{x^2}{A^2} - \frac{y^2}{B^2} = 1\) (a hyperbola) to intersect orthogonally, we need to follow these steps:

### Step 1: Differentiate the first curve
The first curve is given by:
\[ \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \]
Differentiating both sides with respect to \(x\):
...