Hello me and my friend have been trying to figure out whay is wrong with my ciricle formula. When completing a check to see if the formula is correct we get the wrong answer even though we should be edning up with the correct answer. It goes like this:

(the math done here is for my algbra two and trig class) 



Parent fucntion: x+ y= r

a= 9     b= 9 

h=1      k=4  

(x-1)+ (y-4)= 9 

Transformation: (x,y) = (9x+1), (9y+4) 

Equation: y= 4 plus or minus 9 square root 9-(x-1)2  



Point: (x,y) = (1,13) 

(1-1)2 + (y-4)2 = 9

0+ (y-4)= 9 

0 + square root (y-4)= square root 9 

y-4 = 3 

that would equal 7 which does not equal 13. However if I were not to square root 9 I would get 13, But that would be breaking the rules, Can anyone explain what I am doing wrong here? 

 Nov 26, 2017

I'm no expert at this, but notice that you have:


 x^2 + y^2 = r^2  as the "parent function", then further down you have this:


(x-1)^2 + (y-4)^2 = 9   Notice that you are squaring the LHS. Shouldn't you then square the RHS as well? So, when checking it you have this:


(1-1)^2 + (y-4)^2 = 9, but if you squared 9^2 on RHS, then you will have:

y =-5       and       y = 13, which is what you want.

 Nov 26, 2017

I am not squaring the right side of my equatin as It is already squared. I don't  need to put three squared unlike the left side where I need to do some steps before squaring. The right side is already solved. If you rerfer to the parent function x+ y= r2 you'll see that r is squared. Sorry for the confusion.

Guest Nov 26, 2017
edited by Guest  Nov 26, 2017

I believe I figured it out if you use (x-1)2 + (y-4)2 = 9 and plug in 1 for x and 13 for y you will get 3 = 3.

As the x part of the equation equals zero then 13-4 equals 9 sqeared. So you end up with 9= 9. Then just square root them and you get 3 equals 3. 

 Nov 26, 2017

I don't know what your  " a "  and  " b "  stand for, but it looks like you want the equation of a circle with its center at  (1, 4)  that passes through  (1, 13) .


the radius of the circle  =  the distance between the center and a point on the circle

the radius of the circle  =  the distance between  (1, 4)  and  (1, 13)


Notice how the (1, 4)  and  (1, 13)  both have the same  x  coordinate.

So the distance between the two points is just  13 - 4 .


the radius of the circle  =  13 - 4   =   9


So we know that  r = 9  ,  h = 1 ,  and  k = 4 .


Plugging these values directly into the standard form of a circle.....


(x - h)2 + (y - k)2  =  r2


(x - 1)2 + (y - 4)2  =  92


(x - 1)2 + (y - 4)2  =  81        This is the equation of the circle, and here's a graph of it.

 Nov 26, 2017

Thank you what I was looking for was to find the error in my checking of the equation you just wrote. Though I have now figured that out but thank you for your resonse. A stands for the amount dilated horzintoally and b stand for the amount dilated vertically. 

Can someone please close this forum/check that it has been answer?

Guest Nov 26, 2017

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