(a).

The motion of alpha particles as they are shot at a piece of gold foil thick.

Observe the figure :

The angle at which the particles are deflected is .

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Since the particles are deflected at the asymptotes will be .

(b).

Vertex of the path of the alpha particles is .

Since the vertex is from the center of the hyperbola, .

The slope of the asymptotes is given by .

Since .

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The equation of the hyperbola particle path is .

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Substiute and in the standard form of hyperbola .

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The equtaion of hyperbola is .

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(a) The asymptotes will be .

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(b)The equtaion of hyperbola is .

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