How do you find the general form of the equation of a circle with this equation in standard form #(-2-h)^2+(3-k)^2=25#?

1 Answer
May 16, 2016

Answer:

Assuming that the intent of the given equation is that #(x,y)=(-2,3)# is a point on the circumference of the circle and #(h,k)# is the center
then there is no simple standard form equation.

Explanation:

The intent of this question is not completely clear (at least to me).

I have assumed that what we are given is intended to be of the generalized form:
#color(white)("XXX")(x-h)^2+(y-k)^2=r^2#
with given (sample) point for #(x,y)# and radius squared #r^2#
with the objective of finding constants for the center #(h,k)#

However as can been seen in the image below there are multiple (infinite number) of circles with #(x,y)=(-2,3)# as a point on the circumference and radius of #r=5# (i.e. #r^2=25#).

The collection of centers for these circles form a circle themselves at a distance of #5# from the given point #(-2,3)#

enter image source here