# Geometry

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A circle with the equation (x + 3)2 + (y - 2)2 = 25 is reflected over the line x = 2.

What is the equation of the image?

• Geometry -

y does not change
x new = (2-x) + 2 = 4-x
x = 4-xnew

(4-xnew + 3)^2 - (y-2)^2 = 25

(-xnew +7)^2 - (y-2)^2 = 25
same as
(xnew-7)^2 - (y-2)^2 = 25

check
old center was at x = -3
that is 5 to the left of x = 2 line
5 to the right of the line is x = 7
sure enough

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