if the line 2x - y +1 = 0 touches the circle at the point (2,5) and the center of the circle lies on the line x+y -9 =0 find the eqn of circle

If the line 2x - y +1 = 0 touches the circle at the point (2,5) to the center is perpendicular, then

As, the line passes through (2,5) having

It is given that the center of the circle lies on the line x+y -9 =0........(ii)

So, this line passes through the center of the circle.

Put the value of y in (ii), we get,

Now,

Distance from the centre of circle (6,3) to the point (2,5) which touches the circle.

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