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

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​ 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 tan θ = ( 1 − 2 9 ​ 2 − 3 ​ − 3 ​ ) = 7 9 ​ θ = tan − 1 ( 7 9 ​ ) (angle will be acute) ​

Mathematics - Parabola Question with Solution | TestHub

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