# Thread: Help with Arc Formula

1. ## Help with Arc Formula

Hi all,

I've been struggling with this for a few weeks. I'm stumped...hoping to get some help here. Thank you in advance.

Please take a look at the image below.

I need a formula for an arc that passes through a specific point on a line angled at Theta degrees. In this specific example I've assumed that the angle is 45 degrees.

The specific point that the arc will pass through will be at Y units. For this example let's assume that Y is 5.

Any help is greatly appreciated.

Thank you

2. Originally Posted by tspree15
Hi all,

I've been struggling with this for a few weeks. I'm stumped...hoping to get some help here. Thank you in advance.

Please take a look at the image below.

I need a formula for an arc that passes through a specific point on a line angled at Theta degrees. In this specific example I've assumed that the angle is 45 degrees.

The specific point that the arc will pass through will be at Y units. For this example let's assume that Y is 5.

Any help is greatly appreciated.

Thank you

is this what you're looking for (in green) ?

3. Yes, that is exactly what I'm looking for...although I'd like the arc to have a steeper slope towards the Y coordinate.

Any chance you can help come up with a formula?

Thank you

4. Oh sorry, I see you have the formula posted in the top right corner. It's a little too small for me to make out. Would you mind posting a larger version?

5. $y = \sqrt{25 - (x-5)^2}$

6. Originally Posted by skeeter
$y = \sqrt{25 - (x-5)^2}$
I must be doing something wrong. When I plug that into my graphing application I can't find the arc.

Also, where do I specify the 45 degree angle in that formula?

7. is the 45 degree angle between the two lines?

8. The line on the right is at an angle of 45 degrees. The degree is a variable.

What I'm looking for is a formula that will draw an arc through a line of X degrees and a height of Y.

9. If you need any more details please let me know. I'm anxious to find a solution

Thanks

10. I'm afraid you've lost me ... especially with the desire to have the curve "steeper" near the y-coordinate. The "arc" I made is that of a circle.

Is this part of a stated problem or something you have conjured up?

11. Originally Posted by skeeter
I'm afraid you've lost me ... especially with the desire to have the curve "steeper" near the y-coordinate. The "arc" I made is that of a circle.

Is this part of a stated problem or something you have conjured up?
This is for a software program designed to trace the path of a golf ball on the green. I have a formula which tells me the angle that the ball will end up compared to the origin.
For example, if my forumla tells me the angle is 45 degrees, that means that I can draw a line from the ball (origin) at a 45 degree angle and the point equal with the hole (the y coordiante) will be where the ball should end up.

That's pretty much what I've shown in the graph in the first post. The y coordiante is the hole and the angle of offset for the ball path is 45 degrees.

Does this make more sense?

12. Originally Posted by tspree15
This is for a software program designed to trace the path of a golf ball on the green. I have a formula which tells me the angle that the ball will end up compared to the origin.
For example, if my forumla tells me the angle is 45 degrees, that means that I can draw a line from the ball (origin) at a 45 degree angle and the point equal with the hole (the y coordiante) will be where the ball should end up.

That's pretty much what I've shown in the graph in the first post. The y coordiante is the hole and the angle of offset for the ball path is 45 degrees.

Does this make more sense?
what "formula" ?

13. I can't post the formula but it just provides a value for degree of offset. It's a single number...ie: 45.