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Parabolas and Foci

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The parabola C has the equation y^2 = 16x
a. Verify that the point P(4t^2, 8t) is a general point on C.
b. Write down the coordinates of the focus S of C.
c. Show that the normal to C at P has equation y + tx = 8t + 4t^3. The normal to C at P meets the x-axis at the point N.
d. Find the area of triangle PSN in terms of t, giving your answers in its simplest form.

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