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JEE Main202523 Jan 2025Morning ShiftMathematicsParabolaActual

If the line 3 x-2 y+12=0 intersects the parabola 4 y=3 x^2 at the points A and B , then at the vertex of the parabola, the line segment A B subtends an angle equal to

Options

  1. A⁻¹ ( 4 5 )
  2. B⁻¹ ( 9 7 )
  3. C⁻¹ ( 11 9 )
  4. D2 - ⁻¹ ( 3 2 )

Correct answer

B. ⁻¹ ( 9 7 )

Step-by-step solution

aligned & 3 x-2 y+12=0 & 4 y=3 x^2 & 2(3 x+12)=3 x^2 & x^2-2 x-8=0 & x=-2,4 & ~m _ OA =-3 / 2, ~m _ OB =3 & = ( -3 2 -3 1- 9 2 )= 9 7 & = ⁻¹ ( 9 7 ) (angle will be acute) aligned

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