Question

general form of the equation of a circle with its center at (-2, 1) and passing through (-4, 1)?

Answer 1

Standard form equation for a circle with center (h,k) and radius r is:

\(\large(x-h)^{2}+(y-k)^{2}=r^2\)

So you have the center, now you just need the radius. Well, given the center and a point on the circle, the radius is just the distance between those 2 points. so use the distance formula to find the distance between those 2 points, which is your r:

\(\large d=\sqrt{(x_{1}-x_{2})^{2}+(y_{1}-y_{2})^{2}}\)

Then plug your center point coordinates, and your r, back into the circle equation that I gave you above.