If the circles x² + y² + 2b₁y + 1 = 0 and x² + y² + 2b₂y + 1 = 0 cuts orthogonally, then the value of b₁b₂ is?

Dear Student,

Please find below the solution to the asked query :

$$\begin{gathered} \mathrm{COndition} \mathrm{for} \mathrm{orthogonality} \mathrm{is} \\ 2{\mathrm{g}}_1{\mathrm{g}}_2+2{\mathrm{f}}_1{\mathrm{f}}_2={\mathrm{c}}_1+{\mathrm{c}}_2 \\ \mathrm{Here} \\ 0+{\mathrm{b}}_1{\mathrm{b}}_2=1+1=2 \\ {\mathrm{b}}_1{\mathrm{b}}_2=1+1=2 \end{gathered}$$

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