Understanding the Circle Equation: Explained Simply | Roger's Guide

[roger]

Hi

we are learning the circle equation now, but I don't understand it at all

Please can someone explain the equation in a simple way ?

thanks a lot !

Roger

 

[arildno]

Are you talking about:
$$x^{2}+y^{2}=R^{2}$$
or some different creature?
Be more specific; post the equation you're confused about!

 

[roger]

Dear Arildno,

Yes that's the equation which I mean.

there's also different variations on it as well with other terms.
please can you help me


Roger

 

[Hurkyl]

Do you know the geometric definition of a circle?

 

[courtrigrad]

the definition of a circle is the locus of all points equidistant from a given point.

x^2 + y^2 = r^2 is the equation of a circle with radius r, and center at (0,0)

(x-h)^2 + (y-k)^2 = r^2 is the equation of a circle with center (h,k)

Then we also have general equation of conic.

 

[roger]

Do you know the geometric definition of a circle?

No I don't.

I don't actually understand the equation or definition ...Thats the problem.

Arildno mentioned the equation but please can someone explain for me .
Thanks

Roger

 

[Atheist]

A circle can be considered the set of all point that have a certain distance (the radius) from a certain point (the center).

In above case the center is the origin (0,0) and the distance is R. Thus, the cirlce is the set of all points (x,y) which have a distance R from the origin. The distance of a point (x,y) from the origin is sqrt(x² + y²) using Pythagoras, so your condition for a point to be part of the circle is
sqrt(x² + y²) = R
or, when squaring that equation:
x² + y² = R²

 

[Math Is Hard]

Have you tried plotting a "unit circle" on a graph? You can use the equation
x^2 + y^2 = 1

if you let y = 0, then you have two possible solutions for x: 1 and -1
this will give you some coordinates: (1,0) and (-1,0)
if you let x = 0, then you have two possible solutions for y: 1 and -1
this will give you some coordinates: (0,1) and (0, -1)

you can play around with plugging in other numbers between zero and 1 for x and y, and if you plot these, you should see a circle forming on your graph.
I don't know if this will be helpful to you, but I remember going through this exercise when I studied trig and it helped me visualize how this function worked.