- Prove that the collection of all parabolas is invariant under similarity transforms.
- Find all parabolas similar to the parabola .

**Incomplete.**

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Prove that the collection of all parabolas is invariant under similarity transforms

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- Prove that the collection of all parabolas is invariant under similarity transforms.
- Find all parabolas similar to the parabola .

**Incomplete.**

a) Take any parabola. Then fit the coordinate system such that the x axis is the parabola axis, and y is parallel to the directrix. Then we have cartesian equation of the parabola to be (y-y_0) = k(x-x_0)^2. If we replace y=ty and x=tx and t 0, we get (x-x_1)^2=k_1(y-y_1), which is again a parabola.

b) Replacing y=ty and x=tx we get x^2=y/k=Cy.