The General Circle Equation??

Question

x^2 + y^2 = r^2

Is there a such thing as a general circle equation?
Is that it (above)? How does it work?

Thanks much!

Answer 1

That depends on what you mean by general. But for a circle with center (h,k) and radius r, the equation is:

(x - h)² + (y - k)² = r²

Your equation has the center at the origin. That isn't general.

Answer 2

the eqn of a circle whose center is (h,k) and radius is r is: (x-h)^2 + (y-k)^2 = r^2 for the first circle, you have both pieces of information for the second, recall that the mid-point of a diameter is the centre and that the radius is 1/2 of the length of a diameter neway, after plugging values into the equation, expand and simplify to the general form and match coefficients to get values of A D Eand F

Answer 3

I'm not sure of the terminology, but a further generalization of that equation is to move the circle around. It works by adding a shift to the x and y:

(x-x0)^2 + (y-y0)^2 = r^2

the circle can have any radius r, and now any center (x0, y0).

Answer 4

x^2 + y^2 = r^2 is the equation of a circle whose center is (0,0).
A more general equation is (x-h)^2 + (y-k)^2 = r^2 which is the equation of a circle with center at (h,k).

Answer 5

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

x represents x axis
y represents y axis
and r represents the radius of the circle

hope this helps!!!

Answer 6

correct. thats when youre drawing a circle. you do it in trig.

heres the wiki:

http://en.wikipedia.org/wiki/Equation_of_a_circle