Where the line intersects the circle

• Sep 18th 2008, 08:22 PM
maecenasaliquam
Where the line intersects the circle
Prologue:
I am a graphic designer who often creates her own scripts to help with the process. So, I'm not a high-school student. It's been over 20 years since high school geometry (I'm deliberately not counting - I don't want to know). Anyway, I hope one of you wizards will take pity on me dispite my non-student & non-teacher status...(Bow)

Problem:
I'm attempting to calculate the x,y coordinate of a point along a circle at a given angle. (it happens to be the point at which a line radiates from the center of the circle outward). I know the radius of the circle & the center points. I know the angle.

Possibilities:
I tried to take the equation of a circle $(x + h)^2 +(y+k)^2=r^2$ & plug in the equation of the line $y = mx + b$ but my brain fused. Ouch. Any suggestions?

Thank you,
Mae
• Sep 18th 2008, 08:27 PM
icemanfan
If you were going to take the approach that you mentioned, a small nitpick: The equation of the circle is $(x - h)^2 + (y - k)^2 = r^2$. However, there is an easier method. Let the center of the circle be (h, k), and the radius be r. Then:

$x = h + r \cos(\theta)$
$y = k + r \sin(\theta)$

where the angle $\theta$ is measured from the positive x-axis moving counterclockwise.
• Sep 18th 2008, 09:21 PM
maecenasaliquam
Right, derived from the old $c^2=a^2+b^2$.

Many thanks.

Mae