question_answer 96)

Find the maximum area of an isosceles triangle inscribed in the ellipse  with its vertex at one end of the major axis.

Answer:

Let ABC be the isosceles triangle inscribed in the ellipse.                                                    ?.. (1)        Let A = (x, y)             A = Area of                                      (Using (1))                                     = (a + x)3       3(a ? x) = a + x                           (a + x  0)       3a ? 3x = a + x       2a = 4x                   Now             [3(a ? x) 2 (a + x) + 3 (a + x)2 (?1) ? 3(a + x)2]                          Area of  is maximum when x = a/2       Max. Area        square units.