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

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, 10 31 ​, 10 29 ​, 10 21 ​, 10 27 ​

MARKS App · Accepted Answer

Equation of auxiliary circle is $ x 2 + y 2 = 9 Eq u a t i o n o f A M i s \frac{x}{3}+\frac{y}{1}=1 im g src = " h ttp s : // c d n − q u es t i o n − p oo l . g e t ma r k s . a pp / p y q / j e e a ​ d v an ce d / Ho d − r W 6 Z n 2 B 0 o S − 2 r 5 N r P W UUU lN 7 n e I A Y N L N 1 K k t m L Y . or i g ina l . f u ll s i ze . p n g " > b r > O n so l v in g Eq s . ( i ) an d ( ii ) , w e g e tC oor d ina t eso f M=\left(-\frac{12}{5}, \frac{9}{5}ight) N o w , a re a o f 	riangle A O M=\frac{1}{2} 	imes O A 	imes M N =\frac{27}{10}$ sq units

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