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JEE Main202310 Apr 2023Morning ShiftMathematicsEllipseActual

Let the ellipse E : x 2 + 9 y 2 = 9 intersect the positive x - and y -axes at the points A and B respectively. Let the major axis of E be a diameter of the circle C . Let the line passing through A and B meet the circle C at the point P . If the area of the triangle with vertices A , P and the origin O is m n , where m and n are coprime, then m - n is equal to

Options

  1. A16
  2. B15
  3. C17
  4. D18

Correct answer

C. 17

Step-by-step solution

Given, Ellipse E : x 2 + 9 y 2 = 9   . . . . . . . . i Now point A 3 , 0   &   B 0 , 1 which is the intersection of given ellipse with positive axis, So, equation of line passing through A   &   B is given by, L : x 3 + y 1 = 1 ⇒ x = 3 - 3 y   . . . . . . . ii Now equation of Circle with diametric point - 3 , 0   &   3 , 0 is given by, C : x 2 + y 2 = 9   . . . . . . . . iii Let Q be foot of perpendicular from P upon major axis, So, from ii   &

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