If the point lies between the region corresponding to the acute angle between the lines
and
, then
None of these
Let the centre of the circle be Since the circle is tangent to the line
the distance between the centre and this line must be equal to the radius of the circle. The distance between a point (x,y) and the line
is:
Therefore, the equation we need to solve is:
Simplifying this equation, we get:
Squaring both sides of the equation, we get:
Solving for we get:
Substituting into the equation we get the corresponding values of
Therefore, the centres of the circles are
The circle that passes through (1,2) and has a centre is not tangent to the line,
. Therefore, the circle we are looking for must have a centre
and radius
The equation of the circle is:
Simplifying, we get:
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