A circle $S = 0$ is drawn with its centre at $(- 1, 1)$ so as to touch the circle $x^{2} + y^{2} - 4 x + 6 y - 3 = 0$ externally. Find the intercepts made by the circle $S = 0$ on the coordinate axes.

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Solution

REF.Image.
$x^{2} + y^{2} - 4 a c + 6 y - 3 = 0$
centre = (2,-3)
$r = \sqrt{2^{2} + 3^{2} + 3}$
$= 4$
$r + 4 = \sqrt{(2 + 1)^{2} + (1 + 3)^{2}}$
$= 5$
$r = 1$
circle $= (x + 1)^{2} + (y - 1)^{2} = 1$
$x^{2} + y^{2} + 2 x - 2 y + 1 = 0$
Intercept $= 2 \sqrt{g^{2} - c} = 0$
$2 \sqrt{f^{2} - c} = 0$

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