Show that the x- and y-intercepts of the circle ` x^(2) + y^(2)`
` + 2gx + 2fy + c = 0 " are" 2sqrt( g^(2) - c) " and " 2sqrt(f^(2) - e)`
Hence , find the condition that the (i) X-axis (ii) Y-axis
(iii) both X , and Y-axes touch the circle .
Also , find the equation of the Iocus of the centre of the
circle which makes intercepts 2a and 2b on the X - and Y-axis respectively .

Answer

i.e., ` x^(2) - y^(2) = a^(2) - b^(2)`.
This is the equation of the locus of the centre .