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JEE Main20254 Apr 2025Evening ShiftMathematicsEllipseActual

Let for two distinct values of p the lines y=x+p touch the ellipse E : x ^2 4^2 + y ^2 3^2 =1 at the points A and B . Let the line y = x intersect E at the points C and D . Then the area of the quadrilateral A B C D is equal to

Options

  1. A36
  2. B24
  3. C48
  4. D20

Correct answer

B. 24

Step-by-step solution

Point of contact are ( a ^2 ~m a ^2 ~m ^2+ b ^2 , b ^2 a ^2 ~m ^2+ b ^2 ) A ( -16 5 , 9 5 ) B ( 16 5 , -9 5 ) Point D is ( 12 5 , 12 5 ) Area of ABD = 1 2 | array ccc - 16 5 & 9 5 & 1 16 5 & -9 5 & 1 12 5 & 12 5 & 1 array | =12 Area of ABCD is =24 option (2)

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