Thread: 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.

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 is the center of a circle and is a point of the circle then its equation is:

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

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.

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