Help with circle graph

Sirus

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Hi there i'm in highschool doing my second to last year :D


I was working through a text book and i got this question:

A circle, centre (0,0) has a diameter of 7 units long. Write down the equation of this circle. Make sure the equation has whole-number coefficients, can someone please explain to me how to do this questions? I'm having a hard time getting my head around circle graphs. Can anyone explain to me, or hint me how to workout this question? i've done x^2+y^2=49 but i'm not sure if i need to put numbers in front of the x^2 and y^2 to manipulate the circle.


Thank you in advance,
 
Hi there i'm in highschool doing my second to last year :D


I was working through a text book and i got this question:

A circle, centre (0,0) has a diameter of 7 units long. Write down the equation of this circle. Make sure the equation has whole-number coefficients, can someone please explain to me how to do this questions? I'm having a hard time getting my head around circle graphs. Can anyone explain to me, or hint me how to workout this question? i've done x^2+y^2=49 but i'm not sure if i need to put numbers in front of the x^2 and y^2 to manipulate the circle.


Thank you in advance,
Hi. Your equation is correct because the center is at the origin.

When the circle is not centered at the origin, we subtract the coordinates from x and y, per this form:

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

where (h,k) are the coordinates of the center, and r is the radius. :cool:
 
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Hi. Your equation is correct because the center is at the origin.

When the circle is not centered at the origin, we subtract the coordinates from x and y, per this form:

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

where (h,k) are the coordinates of the center. :cool:

the answer is 4x^2+4y^2=49 :( i dont understand why its like that.
 
Oops. I made a common mistake. I read "diameter of 7" but then my mind switched to "radius of 7".

The symbol r in my previous post represents the radius.

x^2 + y^2 = (7/2)^2

x^2 + y^2 = 49/4

They do not want a ratio, on the righthand side, so multiply both sides by 4 to clear the denominator. :cool:
 
Oops. I made a common mistake. I read "diameter of 7" but then my mind switched to "radius of 7".

The symbol r in my previous post represents the radius.

x^2 + y^2 = (7/2)^2

x^2 + y^2 = 49/4

They do not want a ratio, on the righthand side, so multiply both sides by 4 to clear the denominator. :cool:

i kind of get what you mean

If we were to write the full equation it would be y=(x-0)^2 +(y-0)^2=(7/2)^2 (R^2(diameter is 7 so 7/2 is the radius) which is squared)
I dont get how the (7/2)^2 turns into 49/4, did you square both numbers in the brackets like 7^2=49 and 2^2= 4 to get from (7/2)^2 to 49/4? then do you multiple both sides by 4 to get rid of the 4 on the denominator?

could i just write x^2+y^2 = 12.25 instead of multiplying both sides by 4?
 
i kind of get what you mean

If we were to write the full equation it would be y=(x-0)^2 +(y-0)^2=(7/2)^2 (R^2(diameter is 7 so 7/2 is the radius) which is squared)
I dont get how the (7/2)^2 turns into 49/4, did you square both numbers in the brackets like 7^2=49 and 2^2= 4 to get from (7/2)^2 to 49/4? then do you multiple both sides by 4 to get rid of the 4 on the denominator?

could i just write x^2+y^2 = 12.25 instead of multiplying both sides by 4?

Yes. (72)2=7222\displaystyle (\frac{7}{2})^2 =\frac{7^2}{2^2}.

You could leave your answer like you said, but the question did say to have whole-number coefficients.
 
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