Thread: Parametric and implicit equation help

1. 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.

Problem#1: x^2+2x+y^2=0

For the implicit equation I go to the step

x^2+2x+y^2+0y=0

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

2x^2-4x -y^2+2y=0

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.

2. Originally Posted by oriont
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.

Problem#1: x^2+2x+y^2=0

For the implicit equation I go to the step

x^2+2x+y^2+0y=0

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

2x^2-4x -y^2+2y=0

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.
$x^2 + 2x + y^2 = 0$

$x^2 + 2x + 1 + y^2 = 1$

$(x+1)^2 + y^2 = 1$

--------------------------------------

$2x^2-4x -y^2+2y=0$

$2(x^2 - 2x) - (y^2 - 2y) = 0$

$2(x^2 - 2x + 1) - (y^2 - 2y + 1) = 2-1$

$2(x-1)^2 - (y-1)^2 = 1$

3. Originally Posted by skeeter
$x^2 + 2x + y^2 = 0$

$x^2 + 2x + 1 + y^2 = 1$

$(x+1)^2 + y^2 = 1$

--------------------------------------

$2x^2-4x -y^2+2y=0$

$2(x^2 - 2x) - (y^2 - 2y) = 0$

$2(x^2 - 2x + 1) - (y^2 - 2y + 1) = 2-1$

$2(x-1)^2 - (y-1)^2 = 1$
The only problem is it is supposed to be in the form [(x-h)2]/a^2 + [(y-k)^2)]/a^2

4. Originally Posted by oriont
The only problem is it is supposed to be in the form [(x-h)2]/a^2 + [(y-k)^2)]/a^2
It should be obvious that a = b = 1 in the first. And in the second a = 1/sqrt{2} and b = 1.