To show: The angle between the parabola and the line segment FP is equal to the angle between the parabola and the line and the given parabola. That is, .
The equation of the parabola is, .
Let be a point on the parabola with focus .
Let be an angle between parabola and the line segment FP and be the angle between the horizontal line and parabola.
Obtain the slope of the tangent line at is computed as follows,
Differentiate with respect to x,
Thus, the slope of the tangent at is ,.
The slope of the line passing through is computed as follows,
The angle between the tangent line at P and the line is ,
Since the tangent line at is and the value ,
Hence the required result is proved.
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