The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x 2 + 9 y 2 = 9 meets its auxiliary circle at the point M . Then, the area of the triangle w

Question

The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse x 2 + 9 y 2 = 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

TestHub · Accepted Answer

Equation of auxiliary circle is x 2 + y 2 = 9 Equation of A M is 3 x ​ + 1 y ​ = 1 On solving Eqs. (i) and (ii), we get Coordinates of M = ( − 5 12 ​ , 5 9 ​ ) Now, area of △ A OM = 2 1 ​ × O A × MN = 10 27 ​ sq units

Mathematics - Ellipse Question with Solution | TestHub

Options:

Doubts & Discussion

JEE Main (2028)