# How Do You Calculate (X,Y) Coordinates on a Circle with a Given Radius?

• 777funk
In summary, the conversation is about calculating coordinates on a circle with a 10" radius. The speaker suggests using the formula x^2 + y^2 = 10^2 and mentions using sin and cos. They also mention using (x - a)^2 + (y - b)^2 = r^2 for an arbitrary center point. They ask for software recommendations for quick and easy solving.
777funk
I would like to calculate (X,Y) coords on a circle with a 10" radius.

I have some idea on how this can work but I'm not real solid on it. Say the center is (0,10) and I'd like to solve for Y given an arbitrary X. How would I do this? Obviously (10,0) and (-10,0) and (0,-10) and I know that sin and cos are going to come into it but not sure the actual formula here.

Any help would be greatly appreciated.

EDIT: Thinking a little bit sin()=opp/hyp and cos()=adj/hyp. opposite would be my Y travel and adjacent would be my X. And the radius=10. Theta would be 2*pi/?.

It's $x^2 + y^2 = 10^2$. You can do $(x - a)^2 + (y - b)^2 = r^2$ for an arbitrary center point (if the circle is not centered at the origin). In such a case the point (a, b) is your center and 'r' is your radius value.

Ok, thanks. So I WAY over complicated things. Thanks for the help there.

As far as quick easy solving for various points, do you (or anyone else for that matter) have any software recommendations?

Last edited:

## 1. How do you find the center point of a circle?

The center point of a circle can be found by identifying the midpoint of any diameter or by using the formula (h,k) where h is the x-coordinate and k is the y-coordinate of the center.

## 2. What is the equation for finding the x and y coordinates on a circle?

The equation for finding the x and y coordinates on a circle is x = h + rcos(theta) and y = k + rsin(theta), where (h,k) is the center point of the circle, r is the radius, and theta is the angle.

## 3. How do you determine the radius of a circle?

The radius of a circle can be determined by measuring the distance from the center point to any point on the circle's circumference. It can also be calculated using the formula r = sqrt((x-h)^2 + (y-k)^2) where (h,k) is the center point and (x,y) is any point on the circle.

## 4. Can you find the x and y coordinates on a circle without using the center point?

Yes, you can find the x and y coordinates on a circle without using the center point by using the formula x = x0 + rcos(theta) and y = y0 + rsin(theta), where (x0,y0) is any known point on the circle and theta is the angle.

## 5. How can you graph a circle if you only have the center point and radius?

To graph a circle with only the center point and radius, plot the center point and then use the radius as a guide to draw the circle's circumference. You can also plot additional points by using the x and y coordinates formula, x = h + rcos(theta) and y = k + rsin(theta), where (h,k) is the center point and theta is the desired angle.

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