The equation of the image of the circle
by the line mirror 
is
. Find
.
Text Solution
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235 JEE Main 2020
The center of the required circle is the image of the center
with respect to the line
mirror
and radius is equal to the radius of the given circle.
Let
be the image of the point
with respect to the line mirror. Then the mid-point of
the line joining
and
lies on the line mirror.

or 
Also
is perpendicular to 
or 
Solving
and 
Thus, the center of the image circle is
. The radius of the image circle is same as the
radius of
i.e.,
.
Hence the equation of the required circle is
i.e. 
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