# Thread: Parametric equation for the circle..

1. ## Parametric equation for the circle..

Can yo help me in the following questions .I encounter problem in understanding parametric equation for the lines and circles ..and what is the uses of parametric equation

1-obtain parametric equation for the circle S with equation :

X2+y2-2x+4y-4=0

Show that the center of the circle S lies on the line with parametric equations:

x=t, y=-4+2t

2. Originally Posted by Diligent_Learner
Can yo help me in the following questions .I encounter problem in understanding parametric equation for the lines and circles ..and what is the uses of parametric equation

1-obtain parametric equation for the circle S with equation :

X2+y2-2x+4y-4=0

Show that the center of the circle S lies on the line with parametric equations:

x=t, y=-4+2t
Complete the square: $\displaystyle x^2 + y^2 - 2x + 4y - 4 = 0 \Rightarrow (x - 1)^2 + (y + 2)^2 = 9$

$\displaystyle x - 1 = 3 \cos (t) \Rightarrow x = 3 \cos (t) + 1$.

y = y(t) is left for you, as is the range of t.

To answer the second part, substitute the x- and y-coordinates of the circle into the parametric equations for the line and show that you get the same value of t.