The radius of the circle touching the line 2 x+3 y+1=0 at (1,-1) and cutting orthogonally the circle having line segment joining (0,3) and (-2,-1) as diameter is
We are given that line 2x + 3y + 1 = 0 touches the circle S = 0 at (1, – 1).
So, the equation of this circle can be given by
....[i]
But this circle is orthogonal to the circle the extremities of whose diameter are (0, 3) and (–2, –1).
...[ii]
Applying the condition of orthogonality for (i) and (ii),
Substituting this value of in (i), we get the required circle as
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