What is the standard form of the equation of a circle with center (1,2) intersects x-axis at -1 and 3?

1 Answer
Jan 5, 2016

Answer:

#(x-1)^2+(y-2)^2=8#

Explanation:

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

In the case the radius is the distance between the center #(1,2)# and one of the points on the circle; in this case we could use either of the x-intercepts: #(-1,0)# or #(3,0)#
to get (using #(-1,0)#):
#color(white)("XXXXXXXX")r=sqrt((1-(-1))^2+(2-0)^2)=2sqrt(2)#

Using #(a,b) = (1,2)# and #r^2=(2sqrt(2))^2 = 8#
with the general standard form gives the answer above.