# Thread: Standard equation of a circle?

1. ## Standard equation of a circle?

I'm trying to find the standard equation of a circle given the circles center and a point that it passes through. I can't find which formula is actually the "standard." Would it be the Center-Radius form (x-h)^2 + (y-k)^2 = r^2 or the General form
x^2 + y^2 + cx + dy + e = 0. I see the Center-Radius form more commonly used but the general form just yells out standard.

2. Originally Posted by street1030
I'm trying to find the standard equation of a circle given the circles center and a point that it passes through. I can't find which formula is actually the "standard." Would it be the Center-Radius form (x-h)^2 + (y-k)^2 = r^2 or the General form
x^2 + y^2 + cx + dy + e = 0. I see the Center-Radius form more commonly used but the general form just yells out standard.
If $(h,k)$ is the center of a circle and $(p,q)$ is a point of the circle then its equation is: $(x-h)^2+(y-k)^2=(h-p)^2+(k-q)^2.$

3. So the standard equation of a circle is the center-radius form? Thanks.

4. Originally Posted by street1030
I'm trying to find the standard equation of a circle given the circles center and a point that it passes through. I can't find which formula is actually the "standard." Would it be the Center-Radius form (x-h)^2 + (y-k)^2 = r^2 or the General form
x^2 + y^2 + cx + dy + e = 0. I see the Center-Radius form more commonly used but the general form just yells out standard.
The general form is nothing more than the centre-radius form multiplied out.

Pythagoras' theorem describes the circle equation.
The circle is the set of all points with a common distance to the fixed centre.

5. Yes I understand this but the instructions to one of my problems says "Find the standard equation of a circle with the center at (-8,4) and passing through (3,-2)." But in my book they don't mention anything about a "standard form" only the center-radius form and general form. I know how to work them both I just don't want to put it in the wrong form