Question

The minimum area of the triangle formed by any tangent to the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) with the coordinate axes is?

• A. \( a^2 + b^2 \)
• B. \( \left( \frac{a + b}{2} \right)^2 \)
• C. \( ab \)
• D. \( (a - b)^2 \)

Hint:

The area of the triangle formed by a tangent to an ellipse and the coordinate axes is minimized when it is formed at a specific tangent point.

Answer 1

The Correct Option is C

The minimum area of the triangle formed by a tangent to the ellipse and the coordinate axes is \( ab \), which can be derived using geometric properties of the ellipse.