equation of a circle

[gcvbt7t]

x^2+y^2=r^2..... this is an equation of a circle with center at the origin and radius r... can somebody please explian what is the significance of x and y

[chintuz]

x and y are the co-ordinates representing the circle, considering the center of the circle as (0,0).

[gcvbt7t]

are x and y the cord of points within the circle or on the circumference of the circle ?

[chintuz]

on the circumference.

[agarbattis]

and r is the radius of the circle

[DWarrior]

x and y are variables, and the equation shows the relationship between them. Generally x is taken as the independent variable, and the value of y depends on x.

Often y is isolated, but sometimes it makes sense to keep variables in a different order. For example, in the case of a circle the form (x-a)^2+(y-b)^2=r^2 is the most telling: a and b are intercepts and r is the radius. Isolating y would just obfuscate the important parameters.

in the case of an ellipse, the form (x-a)^2/u^2 + (y-b)^2/v^2 =1 makes the most sense because you can immediately extract intercepts and major/minor axis.

Another cool piece of info: (x-a)^2/u^2 i (y-b)^2/v^2 =1 the minus sign in front of y tells you it's a hyperbola instead of an ellipse.

When you get into 3 or more variables, there are analogous forms for different shapes that are more telling than simply isolating one variable.

But I digress.

Function (mathematics) - Wikipedia, the free encyclopedia

[Makumajon]

Hi Warrior, what does "a and b are intercepts" mean in a circle equation?"

[DWarrior]

sorry, I used the wrong term. I meant to say a and b are coordinates of the circle's center.

In the form (x-a)^2+(y-b)^2=r^2, the circle is centered at (a,b) with radius r.

[ankitharish]

was just searching a few concepts on the circle and I found this.
Really good video,be patient for the first few secs and rest is just great.
YouTube - Functions - General Equation of a Circle