Question

The line passing through the extremity A of the
major axis and extremity B of the minor axis of the
ellipse x2 +9y2 = 9 meets its auxiliary circle at the
point M. Then the area of the triangle with vertices
at A, M and the origin O is :-
(IIT-2009)​

Answer 1

Answer:

The line passing through the extremity A of the

major axis and extremity B of the minor axis of the

ellipse x2 +9y2 = 9 meets its auxiliary circle at the

point M. Then the area of the The line passing through the extremity A of the

major axis and extremity B of the minor axis of the

ellipse x2 +9y2 = 9 meets its auxiliary circle at the

point M. Then the area of the triangle with vertices

at A, M and the origin O is :-passing through the extremity A of the

major axis and extremity B of the minor axis of the

ellipse x2 +9y2 = 9 meets its auxiliary

(IIT-2009)The line passing through the extremity A of the

major axis and extremity B of the minor axis of the

ellipse x2 +9y2 = 9 meets its auxiliary circle at the

point M. Then the area of the The line passing through the extremity A of the

major axis and extremity B of the minor axis of the

ellipse x2 +9y2 = 9 meets its auxiliary circle at the

point M. Then the area of the triangle with vertices

at A, M and the origin O is :-passing through the extremity A of the

major axis and extremity B of the minor axis of the

ellipse x2 +9y2 = 9 meets its auxiliary

(IIT-2009)...........

Answer 2

The area of the triangle formed by the vertices A M and O is equal to 2.7 sq units.

• Length of semi major and semi minor axis of the ellipse is equal to 3 and 1 respectively.
• So,the coordinates are A=(3,0) and B=(0,1)
• The equation of the line AB will be x=3-3y.
• The equation of the auxiliary circle of the ellipse is x²+y²=9.
• Equating the line AB with the equation of circle we get the the coordinates of point M to be (-2.4,1.8)
• Hence the area of triangle AMO is equal to 1.8×3/2=2.7