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

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

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Answer 1 · 2016-11-08T01:24:49

${(x - 2 a)}^{2} + {(y - a)}^{2} = 4 a^{2}$ $(x-2a)^2+(y-a)^2=4a^2$

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 $x$ $x$ coordinate of the center of the circle.

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

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

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

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

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