Question

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

Answer 1

`(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`