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STD 11 - 10.1 circle and system of circle — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEESTD 11 - 10.1 circle and system of circle4 Marks
MCQ
If one common tangent of the two circles $x^2 + y^2 = 4$ and ${x^2} + {\left( {y - 3} \right)^2} = \lambda ,\lambda  > 0$ passes through the point $\left( {\sqrt 3 ,1} \right)$, then possible value of  $\lambda$ is
  • ✓
    $\frac{1}{4}$
  • B
    $\frac{1}{2}$
  • C
    $1$
  • D
    $2$
✓

Answer

Correct option: A.
$\frac{1}{4}$
a
Common tangent $\mathrm{T}=0$

$\sqrt{3} x+y=4$

Use $[\perp \text { distance from }(0,3)]^{2}=\lambda$

$\left|\frac{1}{2}\right|^{2}=\lambda \Rightarrow \lambda=\frac{1}{4}$

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