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JEE Advanced 2009Paper 1
Exam
JEE Advanced
Year
2009
Paper
Paper 1
Subject
Mathematics
Chapter
Ellipse

JEE Advanced 2009 · Paper 1 · Mathematics · Ellipse

The line passing through the extremity A of the major axis and...

The line passing through the extremity AA of the major axis and extremity BB of the minor axis of the ellipse x2+9y2=9x^2+9 y^2=9 meets its auxiliary circle at the point MM. Then, the area of the triangle with vertices at A,MA, M and the origin OO isThe 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=9The 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

Options

  1. A3110\frac{31}{10}
  2. B2910\frac{29}{10}
  3. C2110\frac{21}{10}
  4. D2710\frac{27}{10}

Correct answer

D. 2710\frac{27}{10}

Step-by-step solution

Equation of auxiliary circle is x²+y²=9 Equation of AMA M is x3+y1=1<imgsrc="/api/proxy−image?url=https\frac{x}{3}+\frac{y}{1}=1<img src="/api/proxy-image?url=https%3A%2F%2Ffirebasestorage.googleapis.com%2Fv0%2Fb%2Fquantrexacademy-app.firebasestorage.app%2Fo%2Fquestions%252Ffigs%252Fpyq%252Fjee_advanced%252FHod-rW6Zn2B0oS-2r5NrPWUUUlN7neIAYNLN1KktmLY.original.fullsize.png%3Falt%3Dmedia&clean=1&v=wm2" data-qx-orig-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fjee_advanced%2FHod-rW6Zn2B0oS-2r5NrPWUUUlN7neIAYNLN1KktmLY.original.fullsize.png?alt=media" data-qx-storage-src="https://firebasestorage.googleapis.com/v0/b/quantrexacademy-app.firebasestorage.app/o/questions%2Ffigs%2Fpyq%2Fjee_advanced%2FHod-rW6Zn2B0oS-2r5NrPWUUUlN7neIAYNLN1KktmLY.original.fullsize.png?alt=media"> \\ On solving Eqs. (i) and (ii), we get Coordinates of M=(−125,95)Now,areaof△AOM=12×M= \left(-\frac{12}{5}, \frac{9}{5}\right) Now, area of \triangle A O M=\frac{1}{2} \times O A ×\times M N=2710N=\frac{27}{10}sq units
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