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Normals are drawn at points `A, B, and C` on the parabola `y^2 = 4x` which intersect at P. The locus of the point P if the slope of the line joining the feet of two of them is 2, is

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To find the locus of the point P where normals are drawn at points A, B, and C on the parabola \( y^2 = 4x \) and intersect at P, given that the slope of the line joining the feet of two of them is 2, we can follow these steps: ### Step 1: Identify the General Point on the Parabola The parabola \( y^2 = 4x \) can be represented in parametric form. A general point on the parabola can be expressed as: \[ P(t) = (t^2, 2t) \] where \( t \) is a parameter. ...
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