How do you find the equation of the circle with centre (2,5) which touches the x axis?

1 Answer
Jan 14, 2016

Answer:

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

Explanation:

The general form for the equation of a circle is:
#color(white)("XXX")(x-x_c)^2+(y-y_c)^2=r^2#
where #(x_c,y_c)# is the center of the circle
and #r# is the circle's radius.

We are told that #(x_c,y_c)=(2,5)#
and that the circle touches the x-axis.
#rarr# the distance from the center of the circle to the x-axis is #y_c#
#rarr# the radius #r=y_c=5#

Substituting
#color(white)("XXX")2rarr x_c#,
#color(white)("XXX")5rarry_c#, and
#color(white)("XXX")5rarrr#
in the general equation:
#color(white)("XXX")(x-2)^2+(y-5)^2=5^2#