# Finding circle coordinates given center, radius and x value only.

• Jul 22nd 2010, 10:15 AM
stillblazin
Finding circle coordinates given center, radius and x value only.
Center is at 0,1044 why 1044? because of pixels.

Please take a look at my picture now.

I want to find the coordinates of the points on the circle, given the x value: 1 2 3 4 5......... so on.
• Jul 22nd 2010, 10:34 AM
earboth
Quote:

Originally Posted by stillblazin
Center is at 0,1044 why 1044? because of pixels.

Please take a look at my picture now.

I want to find the coordinates of the points on the circle, given the x value: 1 2 3 4 5......... so on.

1. A circle with the center C(h, k) and the radius r is determined by the equation:

$\displaystyle (x-h)^2+(y-k)^2=r^2$

2. With the given data your circle has the equation:

$\displaystyle (x-0)^2+(y-1044)^2 = 1044^2$

3. To get the y-coordinates of a point you only have to plug in the x-value and solve the equation for y:

$\displaystyle x^2+(y-1044)^2 = 1044^2~\implies~|y-1044| = \sqrt{1044^2-x^2}$ which "simplifies" to:

$\displaystyle y=1044+\sqrt{1044^2-x^2}~\vee~y=1044-\sqrt{1044^2-x^2}$

Example: x = 10:

$\displaystyle y = 1044+\sqrt{1044^2-100}~\approx~2087.95~\vee~y = 1044-\sqrt{1044^2-100}~\approx~0.048$