Let C be the curve in the plane defined by .My sketch looks like a figure of 8.a). Draw a sketch of C.

I know that:b). Find the co-ordinates of the four points at which the tangent to C is vertical.

Hint: The formula may be helpful.

Therefore:

Hence:

I want when . This will be when the denominator of my expression is equal to 0.

Since I have an expression for , it is useful to write x and y in terms of .

Therefore when we have:

The first two points are and .

It's also apparent that the next x coordinate is with the same y coordinates as before.

The other two points are and .

The four points are (listed together for clarity) , , and .

I'm pretty sure this is right. I would just like someone to confirm my answer.