The number of integral values of lambda for | vedclass

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Question

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-1

Vedclass · Accepted Answer

$16$

Vedclass · Answer

Here, radius $\sqrt{\left(\frac{\lambda}{2}ight)^{2}+\left(\frac{1-\lambda}{2}ight)^{2}-5 \leq 5} \quad$

$\Rightarrow 2 \lambda^{2}-2 \lambda-119 \leq 0$

$	herefore \frac{1-\sqrt{239}}{2} \leq \lambda \leq \frac{1+\sqrt{239}}{2} $

$\Rightarrow-7.2 \leq \lambda \leq 8.2(	ext { nearly }) $

$	herefore \lambda=-7,-6, \ldots, 8$

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

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