How do you write the equation for a circle with center (2a, a) and touching the y-axis?

1 Answer
Nov 8, 2016

Answer:

#(x-2a)^2+(y-a)^2=4a^2#

Explanation:

If the circle touches the Y-axis then the radius of the circle is equal to the horizontal distance from the Y-axis to the center of the circle.

The distance from the Y-axis to the center of the circle is the #x# coordinate of the center of the circle.

So in this case the radius is #2a#.

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

So the equation for a circle with cneter #(color(red)(2a),color(blue)a)# and radius #color(green)(2a)# is
#color(white)("XXX")(x-color(red)(2a))^2+(y-color(blue)a)^2=color(green)(""(2a))^2#