lf a quadrilateral is formed by four tangents to the ellipse `x^2/9+y^2/4=1` then the area of the square is equal to

Explanation

To find the area of the square formed by the tangents to the ellipse given by the equation \( \frac{x^2}{9} + \frac{y^2}{4} = 1 \), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the parameters of the ellipse**:
The given equation of the ellipse is \( \frac{x^2}{9} + \frac{y^2}{4} = 1 \).
Here, we can identify:
- \( a^2 = 9 \) (thus \( a = 3 \))
- \( b^2 = 4 \) (thus \( b = 2 \))

2. **Find the equation of the director circle**:
The equation of the director circle of the ellipse is given by:
\[ x^2 + y^2 = a^2 + b^2 \]
Substituting the values of \( a^2 \) and \( b^2 \):
\[ x^2 + y^2 = 9 + 4 = 13 \]

3. **Determine the area of the square**:
The area \( A \) of the square formed by the tangents to the ellipse can be calculated using the formula:
\[ A = 2(a^2 + b^2) \]
Substituting the values of \( a^2 \) and \( b^2 \):
\[ A = 2(9 + 4) = 2 \times 13 = 26 \]

4. **Conclusion**:
Therefore, the area of the square formed by the tangents to the ellipse is \( 26 \) square units.

### Summary of the Solution:
The area of the square formed by the tangents to the ellipse \( \frac{x^2}{9} + \frac{y^2}{4} = 1 \) is \( 26 \) square units.

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