Question

If P is a variable point on the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ with foci S and S' and $\Delta$ is the area of triangle SPS' , then the maximum value of $\Delta$ is

• A. $\sqrt{7}$
• B. $2\sqrt{7}$
• C. 3$\sqrt{7}$
• D. 4$\sqrt{7}$

Answer 1

Answer: (C)

3$\sqrt{7}$

Answer 2

Let P = (acosθ, bsinθ)

SS’ = 2ae

The area of ∆PSS’ = $\frac{1}{2}$ (SS’) (perpendicular distance from P to SS’)

= $\frac{1}{2}(2ae)(b\sin\theta)$

∴ Maximum of ∆ PSS’ = abc (since sinθ ≤ 1)

= 4 x 3 x $\frac{\sqrt{7}}{4} = 3\sqrt{7}$.