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Question -

Find the equations of the tangent and normalto the parabola┬аy2┬а= 4ax┬аatthe point (at2, 2at).



Answer -

The equation of the given parabola is┬аy2┬а=4ax.

On differentiating┬аy2┬а=4ax┬аwith respect to┬аx, we have:

тИ┤The slope of the tangent atis┬а

Then, the equation of thetangent atis given by,

y┬атИТ 2at┬а=

Now, the slope of thenormal atis given by,

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

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