If circles {x^2} + {y^2} - 2ax + c = 0 and {x^2} + {y^2} + 2by + 2λ = 0 intersect orthogonally, the

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10-1.Circle and System of Circles

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If the circles ${x^2} + {y^2} - 2ax + c = 0$ and ${x^2} + {y^2} + 2by + 2\lambda = 0$ intersect orthogonally, then the value of $\lambda $ is

A

$c$

B

$-c$

C

$0$

D

None of these

Solution

(d) Condition for circle intersects orthogonally,

$2({g_1}{g_2} + {f_1}{f_2}) = {c_1} + {c_2}$

$ \Rightarrow 0 = c + 2\lambda $

$\Rightarrow \lambda = – \frac{c}{2}$ .

Standard 11

Mathematics

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