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JEE Main202330 Jan 2023Morning ShiftMathematicsStraight LinesActual

A straight line cuts off the intercepts OA = a and OB = b on the positive directions of x -axis and y - axis respectively. If the perpendicular from origin O to this line makes an angle of 6 with positive direction of y -axis and the area of OAB is 98 3 3 , then a ^2- b ^2 is equal to:

Options

  1. A392 3
  2. B196
  3. C196 3
  4. D98

Correct answer

A. 392 3

Step-by-step solution

Plotting the diagram of the given data we get, Equation of straight line Here given O A = a   &   O B = b , so equation of line A B in intercept form will be x a + y b = 1   . . . . . . 1 And given perpendicular line of length p is making π 3 angle with the x - axis, So, the equation of line in normal form will be x cos π 3 + y sin π 3 = p ⇒ x 2 p + y 3 2 p = 1 So, on comparing with the equation 1 we get, a = 2 p   &   b = 2 p 3 Now area of the triangle O A B is

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