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If the angle between the normal to the parabola `y^(2)=4ax` at point P and the focal chord passing through P is `60^(@)`, then find the slope of the tangent at point P.

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To find the slope of the tangent to the parabola \( y^2 = 4ax \) at point \( P \) given that the angle between the normal at \( P \) and the focal chord passing through \( P \) is \( 60^\circ \), we can follow these steps: ### Step 1: Understand the Geometry The parabola \( y^2 = 4ax \) has its focus at the point \( (a, 0) \). The normal at point \( P \) and the focal chord passing through \( P \) form an angle of \( 60^\circ \). ### Step 2: Identify the Slope of the Normal Let the coordinates of point \( P \) on the parabola be \( (at^2, 2at) \) where \( t \) is the parameter. The slope of the tangent at point \( P \) can be derived from the derivative of the parabola. ...
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