Question

If the latusrectum of the ellipse x²tan²α + y²sec²α = 1 is ½, then α =

• A. π/12
• B. π/6
• C. 5π/12
• D. π/6

Answer 1

Answer: (A)

π/12

Answer 2

Length of latusrectum = $\frac{2b^{2}}{a} = \frac{1}{2}$

4b² = a

4.cos²α = cotα

⇒ sin2α = ½

⇒ 2α = π/6

⇒ α = π/12