# Find positive y intercept of a circle given a radius of 1 and x intercepts of +/-(.580/2).

#### Jordanmiller1029

##### New member
I want to make sure I’ve interpreted this correctly. I have some doubts. This is a real-world problem with actual consequences and I haven’t used this kind of math in a long time. I need to be sure.

I need to find the positive Y intercept of a circle given a radius of 1 and x intercepts of +/-(.580/2). My math is below. Please let me know if this is the correct interpretation. TIA

For x,y, use an x intercept of .290,0.

H will be 0 by definition

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

(.290–0)^2+(0-k)^2=1^2

.290^2+(-k)^2=1

.0841+(-k)^2=1

(-k)^2=.9159

-k=.957

k=-.957

-.957+/-1=.043, -1.957

Positive y intercept=.043

Is this a correct application of the formula? Thanks

#### Steven G

##### Elite Member
H will be 0 by definition. OK, fine H will be 0 by definition. Got it. Now can you please define the definition of H??
Since h=k=0 (you really should define your variables) it follows that the center of the circle is at (0,0). You never stated this fact as being given. Was not including that information a typo or are you making a wrong assumption about where the center is?
If the circle is centered at (0.0) and has a radius of 1, then the equation of the circle is x^2 + y^2 =1. Four points on the circle are at (1,0), (-1.0), (0,1) and (0,-1) and these points are the four intercepts. Not sure where the y intercept is at .043.

• stapel

#### Jordanmiller1029

##### New member
H will be 0 by definition. OK, fine H will be 0 by definition. Got it. Now can you please define the definition of H??
Since h=k=0 (you really should define your variables) it follows that the center of the circle is at (0,0). You never stated this fact as being given. Was not including that information a typo or are you making a wrong assumption about where the center is?
If the circle is centered at (0.0) and has a radius of 1, then the equation of the circle is x^2 + y^2 =1. Four points on the circle are at (1,0), (-1.0), (0,1) and (0,-1) and these points are the four intercepts. Not sure where the y intercept is at .043.
I never said h=k at all.

I thought h,k was the universal representation for the x,y coordinate of the center. And since I need a y intercept, h would be zero by definition of that. If that's not a widely recognized formula, I apologize. H,K is the x,y of the center of the circle. And I already gave you the x intercepts. So I'm assuming you didn't bother to really read the post

#### The Highlander

##### Full Member
I want to make sure I’ve interpreted this correctly. I have some doubts. This is a real-world problem with actual consequences and I haven’t used this kind of math in a long time. I need to be sure.

I need to find the positive Y intercept of a circle given a radius of 1 and x intercepts of +/-(.580/2). My math is below. Please let me know if this is the correct interpretation. TIA

For x,y, use an x intercept of .290,0.

H will be 0 by definition

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

(.290–0)^2+(0-k)^2=1^2

.290^2+(-k)^2=1

.0841+(-k)^2=1

(-k)^2=.9159

-k=.957

k=-.957

-.957+/-1=.043, -1.957

Positive y intercept=.043

Is this a correct application of the formula? Thanks
My interpretation of your problem would be this:-

The positive y-intercept of your circle would lie 1 (unit) above the point C (the centre of the circle) on the y-axis, the coordinates of C being (0, h).

As@Steven G has helpfully pointed out, you are not "defining" things very well and appear to have got a bit muddled in your calculations.

Hope that helps. Last edited by a moderator:
• Jordanmiller1029

#### Jordanmiller1029

##### New member
My interpretation of your problem would be this:-

The positive y-intercept of your circle would lie 1 (unit) above the point C (the centre of the circle) on the y-axis, the coordinates of C being (0, h).

By Pythagoras...$1^2=0.29^2+h^2\\\implies h^2=1-0.29^2=0.9159$
Therefore your y-intercept will lie at...$1+\sqrt{0.9159}$
I suspect that was what you were attempting to do yourself but, as @Steven G has helpfully pointed out, you are not "defining" things very well and appear to have got a bit muddled in your calculations.

Hope that helps
Ok, this looks like the same answer I got just with the positive and negatives reversed. Yeah I'm not someone who uses this kind of math often. I don't know all of the correct terms. Thank you for your help

#### The Highlander

##### Full Member
Two possible y-intercepts > 0

View attachment 35831
Indeed! Hadn't thought of that. And that would make his/her original "solution" (0.043 to 3 d.p.) a correct one, too. • Jordanmiller1029

#### Steven G

##### Elite Member
I never said h=k at all.

I thought h,k was the universal representation for the x,y coordinate of the center. And since I need a y intercept, h would be zero by definition of that. If that's not a widely recognized formula, I apologize. H,K is the x,y of the center of the circle. And I already gave you the x intercepts. So I'm assuming you didn't bother to really read the post
Fine, you never said that h=k. You are correct about that. However by saying h=0 and k=0 you are basically saying that h=k(=0).

Which is the center of the circle, (h,k) or (H,K)?

You have the equation (x-h)^2 + (y-k)^2 = 1. If you want to find the y intercept you let x=0, NOT k=0 (or K=0) or h=0 (or H=0)!

I 100% read every word that you wrote. I don't like when someone accuses be of something without any real evidence.
My question to you is did you read my posts? Based on what you gave us, I listed the four intercepts intercepts and none are what you listed. Where is the mistake in my post and/or where is the mistake in your post?

#### Jordanmiller1029

##### New member
Fine, you never said that h=k. You are correct about that. However by saying h=0 and k=0 you are basically saying that h=k(=0).

Which is the center of the circle, (h,k) or (H,K)?

You have the equation (x-h)^2 + (y-k)^2 = 1. If you want to find the y intercept you let x=0, NOT k=0 (or K=0) or h=0 (or H=0)!

I 100% read every word that you wrote. I don't like when someone accuses be of something without any real evidence.
My question to you is did you read my posts? Based on what you gave us, I listed the four intercepts intercepts and none are what you listed. Where is the mistake in my post and/or where is the mistake in your post?
Dude, I also never said k=0. Please stop commenting on my stuff