Get Answers to all your Questions

header-bg qa

The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse \mathrm{x^2+9 y^2=9} meets its auxiliary circle at the point M. Then the area of the triangle with vertices at \mathrm{A, M} and the origin O is

Option: 1

\frac{31}{10}


Option: 2

\frac{29}{10}


Option: 3

\frac{21}{10}


Option: 4

\frac{27}{10}


Answers (1)

best_answer

The ellipse is \mathrm{\frac{x^2}{9}+\frac{y^2}{1}=1}

Its auxiliary circle is \mathrm{x^2+y^2=9}                                       ......(1)
The equation of AB is  \mathrm{\frac{x}{3}+\frac{y}{1}=1 \Rightarrow x+3 y=3 }        ......(2)

Eliminating x between (1) and (2), we get \mathrm{M\left(-\frac{12}{5}, \frac{9}{5}\right)}

Area of triangle  \mathrm{A O M=\frac{1}{2} \cdot A O \cdot M N=\frac{1}{2} \cdot 3 \cdot \frac{9}{5}=\frac{27}{10}} sq. units

Posted by

Info Expert 30

View full answer

JEE Main high-scoring chapters and topics

Study 40% syllabus and score up to 100% marks in JEE