Lengths of tangents from a fixed point to three circles of coaxial system are {t₁},{t₂},{t₃} a

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10-1.Circle and System of Circles

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The lengths of tangents from a fixed point to three circles of coaxial system are ${t_1},{t_2},{t_3}$ and if $P, Q$ and $R$ be the centres, then $QRt_1^2 + RPt_2^2 + PQt_3^2$ is equal to

A

$1$

B

$2$

C

$3$

D

$0$

Solution

(d) Co-axial system ${x^2} + {y^2} + 2gx + c = 0$, ($g$ variable)

$L.H.S.$ = $\Sigma ({g_2} – {g_3})({h^2} + {k^2} – c + 2{g_1}h) = 0$

Since $\Sigma ({g_2} – {g_3}) = 0$

and $\Sigma {g_1}({g_2} – {g_3}) = 0$.

Standard 11

Mathematics

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