Since this family of lines touch a circle for all values of theta, put theta = 0 , pi/2 , -pi/2 , pi .
In the above 4 cases , you will get x=2, y=2 , y=1 , x=1 respectively.
Since the above 4 lines are tangents to the required circle, we can say that
the circle has centre at (3/2,3/2) and has radius 1/2.
So the equation of thwe circle is
Thanks for telling me the method. But i thnk u made a mistake in the calculations. wen theta is put as 0 or pi/2, dont v gt x=3, and y =3 respectively?
o yes i'm sorry for the mistake
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