How do you find the equation of a circle if the centre of the circle is (5,13) and touches the x axis?

1 Answer
Feb 4, 2016

Answer:

#(x-5)^2+(y-13)^2=13^2#

Explanation:

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

If the center of the center of a circle is at #(color(red)(5),color(blue)(13))# and it is tangent to the X-axis
then its radius is the distance from the center to the X-axis,
i.e. the #y# coordinate of its center (in this case #color(green)(13)#)