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# What's wrong with this formula?

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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)

Circle:

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

Check:

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?

Guest Nov 26, 2017
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#1
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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.

Guest Nov 26, 2017
#2
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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
#3
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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.

Guest Nov 26, 2017
#4
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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.

hectictar  Nov 26, 2017
#5
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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.