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10.1 circle and system of circle — MATHS STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceMATHS10.1 circle and system of circle1 Mark
MCQ
The value of $\lambda $, for which the circle ${x^2} + {y^2} + 2\lambda x + 6y + 1 = 0$, intersects the circle ${x^2} + {y^2} + 4x + 2y = 0$ orthogonally is
  • A
    $\frac{{ - 5}}{2}$
  • B
    $ - 1$
  • C
    $\frac{{ - 11}}{8}$
  • ✓
    $\frac{{ - 5}}{4}$
✓

Answer

Correct option: D.
$\frac{{ - 5}}{4}$
d
(d) If two circles ${x^2} + {y^2} + 2{g_1}x + 2{f_1}y + {c_1} = 0$ and $2({g_1}{g_2} + {f_1}{f_2}) = {c_1} + {c_2}$ intersect orthogonally then,

they must follow $2({g_1}{g_2} + {f_1}{f_2}) = {c_1} + {c_2}$ and ${g_1} = \lambda ,\,{f_1} = 3,\,{c_1} = 1$

and ${g_2} = 2,\,{f_2} = 1,\,{c_2} = 0$

So, $2\,(2\lambda + 3) = 1 + 0$

$\Rightarrow 2\lambda + 3 = \frac{1}{2}$

$ \Rightarrow \lambda = \frac{{ - 5}}{4}$.

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