Which is "the" formula of a circle?

Question

Hi!
There are supposedly two formals for x^2+y^2=r^2 and A = pi r^2. What exactly is the difference between these and which is the most appropriate one to use? In other words which would you consider as "the" formula for a circle
Thanks

Answer 1

The formula of a circle depends on the coordinate system used to represent a circle.  The most commonly thought of are cartesian, polar, and spherical.  There are others, hyperbolic, projective, ...



Its straightforward to transform a circle described by a formula from one system of coordinates to another.

Answer 2

x^2 + y^2 = r^2 is the equation for the circle

the general equation is actually 



(x-h)^2 /r^2 + (y-k)^2 /r^2 = 1



Similar to the equation for an ellipse -- the circle is a special form of the conic figure called the ellipse. (h,k) is the centre of the circle.



Note: that's in cartesian coordinates. In polar coordinates, it's just "r = R" (the locus is all points at distance R from the centre)



A = π r^2 is the formula for the area of the circle. Use this to find the area of a circle when needed; don't need to know the centre.



 and P = 2πr is the formula for the circumference Use this to find the circumference (or perimeter) length

Answer 3

go back to school and learn . simple question and you dont know the answer , 2 x r  x  pi  = A or diameter x pi = A or as i was yaught 2 pi r = A

Answer 4

the first exquation is the cartesian plot of the circle 



x^2 + y^2 = r^2



polar coordinates of  a circle 



r where r is a vector 



that is more convenient to use



the second one is the  area of a circle  based on its radius



Area = pi r^2

Answer 5

 The equation of a circle centered in the origin 

 having radius r is x^2 + y^2 = r^2.

 The area of a circle is given by:

 A = π ∙ r2 or A = π ∙ (d/2)2

 π defines the ratio of any circle's circumference to its   diameter and is approximately equal to 3.141593, 

 however the value 3.14 is often used.

Answer 6

a) 6.15 two times

(●|○)

Answer 7

x^2 + y^2 = r^2 is the equation to use ,when working in the Cartesian Coordinate plane. 

A = pi r^2  is the equation to use when calculating the Area, or the radius, 

r^2 = A/pi 

 However, you can then substitute x^2 + y^2 = A/pi 



NB Circles don't have 'formulas'. If there is an equals (=) sign , they are 'EQUATIONS'. 

Answer 8

Pi X Radius squared to get surface area.

Answer 9

x^2 + y^2 = r^2

will give you all the (x, y) points that belong to a circle of radius "r", centred on the origin (0, 0).



If the centre of the circle is at a point other than the origin,

for example, if the centre is at (x, y) = (a, b)

(where a and b are numbers)

then the complete equation is

(x - a)^2 + (y - b)^2 = r^2



Once you are given the values of r, a and b,

the (x, y) solutions to the equation give you all the points that belong to the circumference of the circle.



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In plane geometry (geometry on a flat surface), the properties of the circle can be found using basic formulas.



The basic element of a circle is its radius (r). Once you are given the value of r, you can find the length of the circumference with

Circ. = 2 π r

where π (the Greek letter "pi") is a fixed value (approx. 3.1416)



and you can find the Area of the circle with



A = π r^2



if the length of the radius is given in inches (for example), then the Area will come out in square inches. If r is given in metres, then the area will come out in square metres. And so on.



---



Therefore, each one is "the" formula... depending on what you are looking for.

Answer 10

x^2+y^2=r^2 is the equation of a circle of radius r in two dimensions.  All of the ordered pairs (x, y) that are solutions to this equation are the coordinates of a point on the circle.



A = pi r^2 is the formula for the area of a circle or radius r.   It's not the equation of  a circle.

Answer 11

x^2+y^2=r^2

describes the locus of a point P(x,y) moving around a closed

path which we call it the circle. This circle has a centre at (0,0)

& a radius r. In short, this is a "formula for the shape of this

particular circle". The general one is (x-a)^2+(y-b)^2=r^2, where

(a,b) is the centre & a, b are arbitrary. It is also called the form

of a circle in the rectangular coordinates system.



A=pi(r^2) is a formula to calculate the area of a circle with the

radius r.

Answer 12

One of those is to calculate the area of a circle. 

That's A = π r²

The other one: x² + y² = r² tells you how to graph a circle. 

Answer 13

The two I know will tell you the circumference and the area.

Answer 14

Raymond has a the best answer. A circle may be offset from the origin (0,0) in which case you have to subtract the position (A,B) of the circle center:



(X-A)²+(Y-B)²=R²



The formula A=πR² finds the area but does not define the circle.

Answer 15

The only way you could say that is by deliberately making up BS.  Go away troll.  You can't even be original or funny.

Answer 16

The first equation is the analytical definition of a circle. The second tells you how to calculate the area of a circular region.

Answer 17

"The"  **equation** for a circle is  x^2 + y^2 = r^2 

which defines the locus of points on a circle centred on the origin, radius r.



but there are any many formulas of circles. The other one you quote is for the area, there is 2 pi r or pi d for the circumference 

Answer 18

The first (f(x,y)=r^2) describes the location of the points on the circle (the line forming the perimeter, or circumference, of the circle.  A=pi*r^2 yields the area contained within the line described by the first equation.  The length of that line described by the first function is given by 2*pi*r.



Different things are being described.