Geometry/CIRCLE

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Question
a circle of radius 4 units touches the coordinate axes in first quadrant . find the equations of its imageswith respect to the line mirrors x=0 and y =0

Answer
Since it touches both of the axis and is still in the 1st quadrant, that means it must be tangent to both of the axis.  This means the radius of the circle that touches an axis is perpendicular to that axis.  Since the radius is 4 and the circle is tangent to both axis, that puts the center of the circle 4 units away from each axis, and the only point like that is (4,4).

That makes the equation of the circle be (x-4)+(y-4)=4.
Since 4 = 16, that is (x-4)+(y-4)=16.

That puts the center of the mirrored image over the x axis at (4,-4) and
the center of the mirrord image over the y axis at (-4,4).
This makes the equation mirrored over the x axis be (x+4)+(y-4)=16 and
the equation mirror over the y axis be (x-4)+(y+4)=16.

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