JEE Advance - Mathematics (2004 - No. 4)
where, $${\rm{z = x + iy, }}\alpha {\rm{ = }}\,{\alpha _1}{\rm{ + i}}{\alpha _2}{\rm{,}}\,\beta = {\beta _1}{\rm{ + i}}{\beta _2}{\rm{ }}$$
Centre = $$\frac{{\alpha + {k^2}\beta}}{{1 + {k^2}}}$$, radius = $$\frac{k}{{\left| {1 + {k^2}} \right|}}left| {\alpha + \beta } \right|$$
Centre = $$\frac{{\alpha - {k^2}\beta}}{{1 - {k^2}}}$$, radius = $$\frac{k}{{\left| {1 - {k^2}} \right|}}left| {\alpha - \beta } \right|$$
Centre = $$\frac{{\alpha + {k}\beta}}{{1 + {k}}}$$, radius = $$\frac{1}{{\left| {1 + {k}} \right|}}left| {\alpha - \beta } \right|$$
Centre = $$\frac{{\alpha - {k}\beta}}{{1 - {k}}}$$, radius = $$\frac{1}{{\left| {1 - {k}} \right|}}left| {\alpha + \beta } \right|$$
Centre = $$\frac{{\beta - {k^2}\alpha}}{{1 - {k^2}}}$$, radius = $$\frac{k}{{\left| {1 - {k^2}} \right|}}left| {\alpha - \beta } \right|$$
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