Parametric and implicit equation help
I am trying to do a couple of implicit and parametric problems for hyperbolas, ellipses and circles.
I must be confusing myself because I think I am missing a concept.
For the implicit equation I go to the step
I then complete the square to get
(x-1)^2 + (y-0)^2 =1
Which I put into the form
((x-1)^2)/1^2 + ((y-0)^2)/1^2 =1
from the above implicit equation it appears to be an ellipse with A=1, B=1, H=1, K=0, Center= (1,0) And parametric equation of x=1+1cosT, y=0+1sinT
Question #1 I feel like I am doing something wrong, I believe I got 1 on the right side of the equation because of (?) not entirely sure.
Problem #2: 2x^2+2y=y^2+4x
For the implicit equation I bring the right side over to the left
I then factor
2 (x^2-2x) -y^2+2y=0
Divide the 2 out of both sides and complete the squares
(x-1)^2 - (y-1)^2 =1
put it in the final form
((x-1)^2)/1^2 - ((y-1)^2)/1^2 =1
From the implicit equation it appears to be a hyperbola opening left and right
A=1, B=1, Center= (1,1), Parametric equation of x=1+1secT, y=1+1tanT
Any help would be appreciated.