For #2, we could solve for y and differentiate, but let's do it implicitly.

..............[1]

Divide by y' and get:

Now, take the limit:

Sub into [1]:

Solve for x and we get

That leaves

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ ~~~~~~~~~~~~~~~~~~~~~~

Let's do it using 'regular' differentiation and see if we get the same thing.

Solve for y and get:

Differentiate:

Set the denominator to 0 and solve for x:

We can see that

Plugging this into y, we see

I showed you this so you may know how to find a vertical tangent in the future. Study both methods. They may come in handy.