Circles {(x + a)^2} + {(y + b)^2} = {a^2} and {(x + α )^2} + {(y + β )^2} = {β ^2} cut orthogonal

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10-1.Circle and System of Circles

medium

Circles ${(x + a)^2} + {(y + b)^2} = {a^2}$ and ${(x + \alpha )^2}$ $ + {(y + \beta )^2} = $ ${\beta ^2}$ cut orthogonally, if

A

$a\alpha + b\beta = {b^2} + {\alpha ^2}$

B

$2(a\alpha + b\beta ) = {b^2} + {\alpha ^2}$

C

$a\alpha + b\beta = {a^2} + {b^2}$

D

None of these

Solution

(b) Apply ${({C_1}{C_2})^2} = r_1^2 + r_2^2$ or $2{g_1}{g_2} + 2{f_1}{f_2} = {c_1} + {c_2}$.

Standard 11

Mathematics

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