What is the general form of the equation of a circle given the Center (-1,2) and Solution Point (0,0)?

1 Answer
Dec 11, 2015

Answer:

#(x+1)^2+(y-2)^2=5#

Explanation:

The general form for a circle with center #(a,b)# and radius #r# is
#color(white)("XXX")(x-a)^2+(y-b)^2=r^2#

With center #(-1,2)# and given that #(0,0)# is a solution (i.e. a point on the circle),
according to the Pythagorean Theorem:
#color(white)("XXX")r^2=(-1-0)^2+(2-0)^2 = 5#

and since the center is #(a,b)=(-1,2)#

by applying the general formula we get:
#color(white)("XXX")(x+1)^2+(y-2)^2=5#