For #2, we could solve for y and differentiate, but let's do it implicitly.
Divide by y' and get:
Now, take the limit:
Sub into :
Solve for x and we get
Let's do it using 'regular' differentiation and see if we get the same thing.
Solve for y and get:
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.