Conic Sections: JEE Mains 2022 June 29 Shift 2

Hard· Tangents and normals· +4 / −1
Let P:y2=4axP:y^2=4ax, a>0a>0 be a parabola with focus SS. Let the tangents to the parabola PP make an angle of π4\dfrac\pi4 with the line y=3x+5y=3x+5 touch the parabola PP at AA and BB. Then the value of aa for which AA, BB and SS are collinear is :
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