Find the equations of the tangent and normal to the parabola y² = 4ax at the point (at², 2at).

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Solution

The equation of the given parabola is y² = 4ax.

On differentiating y² = 4ax with respect to x, we have:

∴The slope of the tangent atis

Then, the equation of the tangent atis given by,

y − 2at =

Now, the slope of the normal atis given by,

Thus, the equation of the normal at (at², 2at) is given as:

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