Question

Let p be a variable point on the ellipse x225+y216=1 with foci at s and s'. If a be the area of triangle pss', then the maximum value of a is

Answer 1

Answer:

x²/25 + y²/16 = 1

x²/5² + y²/4² = 1

This is a horizontal ellipse with center (0, 0)

co-vertices (0, -4) and (0, 4)

c = √(25-16)

= 3

foci S(-3, 0) and S'(3, 0)

∆PSS' has base of length 6

max height of ∆PSS' is 4

max area of ∆PSS' = 12 units²