Plz fast 9 The ratio of the areas of triangle inscribed in ellipse x2a2+y2b2=1 to that of triangle - Maths - Conic Sections

Question

Plz fast

9   The   ratio   of   the   areas  
of   triangle   inscribed   in   ellipse  
x 2 a 2 + y 2 b 2 = 1   to   that   of  
triangle   formed   by   the   corresponding
points   on   the   auxiliary   circle  
is   1 2 , then   the   eccentricity   of
  the   ellipse   is ( a )   1 2    
            ( b )   3 2 ( c )
  1 2           ( d )   1 3

Aarushi Mishra · Accepted Answer

E:x2a2+y2b2=1Property: Area of any geometrical shape inscribed in an ellipse is ba times the area of the geometrical shape formed by correpsoinding points on the aunxillary circle of the ellipseArea of triangle inscribed in ellipse=ba Area of triangle formed by corresponding points on the auxillary circleGivenArea of triangle inscribed in ellipse=12 Area of triangle formed by corresponding points on the auxillary circleThereforeba=12We knowb2=a21-e21-e2=b2a2=ba2=141-e2=14e2=1-14=34e=32

Plz fast 9 . The ratio of the areas of triangle inscribed in ellipse x 2 a 2 + y 2 b 2 = 1 to that of triangle formed by the corresponding points on the auxiliary circle is 1 2 , then the eccentricity of the ellipse is ( a ) 1 2 ( b ) 3 2 ( c ) 1 2 ( d ) 1 3