Let the focal chord PQ of the parabola y 2 = 4 x make an angle of 6 0 ∘ with the positive x -axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, S being the focus of the

Question

Let the focal chord PQ of the parabola y 2 = 4 x make an angle of 6 0 ∘ with the positive x -axis, where P lies in the first quadrant. If the circle, whose one diameter is PS, S being the focus of the parabola, touches the y -axis at the point ( 0 , α ) , then 5 α 2 is equal to :

TestHub · Accepted Answer

tan 6 0 ∘ = t 2 − 1 2 t − 0 ​ = 3 ​ ⇒ t = 3 ​ ∴ P ( 3 , 2 3 ​ ) Circle : ( x − 1 ) ( x − 3 ) + ( y − 0 ) ( y − 2 3 ​ ) = 0 at x = 0 ⇒ 3 + y 2 − 2 3 ​ y = 0 ⇒ y = 3 ​ = α 5 α 2 = 15

Mathematics - Parabola Question with Solution | TestHub

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