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10-1.Circle and System of Circles
medium
$\lambda $ का वह मान जिसके लिये वृत्त ${x^2} + {y^2} + 2\lambda x + 6y + 1 = 0$ व ${x^2} + {y^2} + 4x + 2y = 0$ लम्बवत् प्रतिच्छेदित करते हैं, है
A
$\frac{{ - 5}}{2}$
B
$ - 1$
C
$\frac{{ - 11}}{8}$
D
$\frac{{ - 5}}{4}$
Solution
(d)यदि दो वृत्त ${x^2} + {y^2} + 2{g_1}x + 2{f_1}y + {c_1} = 0$ व $2({g_1}{g_2} + {f_1}{f_2}) = {c_1} + {c_2}$ लम्बकोणीय प्रतिच्छेद करते हैं,
तब $2({g_1}{g_2} + {f_1}{f_2}) = {c_1} + {c_2}$ व ${g_1} = \lambda ,\,{f_1} = 3,\,{c_1} = 1$, ${g_2} = 2,\,{f_2} = 1,\,{c_2} = 0$
अत: $2\,(2\lambda + 3) = 1 + 0 $
$\Rightarrow 2\lambda + 3 = \frac{1}{2}$
$ \Rightarrow \lambda = \frac{{ – 5}}{4}$.
Standard 11
Mathematics
