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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
The number of integral values of $\lambda $ for which $x^2 + y^2 + \lambda x + (1 - \lambda )y + 5 = 0$ is the equation of a circle whose radius cannot exceed $5$ , is
  • A
    $14$
  • B
    $18$
  • ✓
    $16$
  • D
    None of these
✓

Answer

Correct option: C.
$16$
c
Here, radius $\sqrt{\left(\frac{\lambda}{2}\right)^{2}+\left(\frac{1-\lambda}{2}\right)^{2}-5 \leq 5} \quad$

$\Rightarrow 2 \lambda^{2}-2 \lambda-119 \leq 0$

$\therefore \frac{1-\sqrt{239}}{2} \leq \lambda \leq \frac{1+\sqrt{239}}{2} $

$\Rightarrow-7.2 \leq \lambda \leq 8.2(\text { nearly }) $

$\therefore \lambda=-7,-6, \ldots, 8$

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