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.