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a) Show that an affine transformation can map a circle to an ellipse, but cannot map an ellipse to a hyperbola or parabola. (b) Prove

a) Show that an affine transformation can map a circle to an ellipse, but cannot map an ellipse to a hyperbola or parabola. (b) Prove that under an affine transformation the ratio of lengths on parallel line segments is an invariant, but that the ratio of two lengths that are not parallel is not.

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