Question

Tangent is drawn to ellipse $\frac{x^{2}}{27}$+ y² = 1 at (3$\sqrt{3}$cos θsin θ) where θ∈ (0, π/2). Then the value of θ such that sum of intercepts on axes made by this tangent is minimum, is

• A. π/3
• B. π/6
• C. π/8
• D. π/4

Answer 1

Answer: (B)

π/6

Answer 2

$\frac{x\cos\theta}{3\sqrt{3}}$ + y sin θ = 1

Sum of intercepts = 3$\sqrt{3}$ sec θ + cosec θ = f (θ), (say)

F'(θ) = $\frac{3\sqrt{3}\sin^{3}\theta - \cos^{3}\theta}{\sin^{2}\theta\cos^{2}\theta}$. At θ = $\frac{\pi}{6}$, f(θ) is minimum.