Question

Minimum area of the triangle formed by any tangent to the ellipse x²/a² + y²/b² = 1 with coordinates axes is –

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

Answer 1

Answer: (C)

ab

Answer 2

equation of tangent at (a cos q, b sin q)

= 1

area A = $\frac{1}{2}$ (a sec q) (b cosec q)

A = $\frac{ab}{\sin 2\theta}$

minimum = ab (Q (sin 2q) maximum = 1)