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JEE Main202430 Jan 2024Morning ShiftMathematicsStraight LinesActual

A line passing through the point A ( 9 , 0 ) makes an angle of 30 ° with the positive direction of x -axis. If this line is rotated about A through an angle of 15 ° in the clockwise direction, then its equation in the new position is

Options

  1. Ay 3 - 2 + x = 9
  2. Bx 3 - 2 + y = 9
  3. Cx 3 + 2 + y = 9
  4. Dy 3 + 2 + x = 9

Correct answer

A. y 3 - 2 + x = 9

Step-by-step solution

Given, A straight line passes through A 9 , 0 and makes a angle 30 ° with the x - axis, And it is rotated by 15 ° degree clockwise So, the new angle with the x - axis will be θ = 30 ° - 15 ° = 15 ° Hence, the equation of the line will be, y - 0 = tan 15 ° x - 9 ⇒ y = tan 45 ° - 30 ° x - 9 ⇒ y = 1 - 1 3 1 + 1 3 x - 9 ⇒ y = 2 - 3 x - 9

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