The number of integral values of $\lambda$ for which $\mathrm{x}^{2}+\mathrm{y}^{2}+\lambda \mathrm{x}+(1-\lambda) \mathrm{y}+5=0$ is the equation of a ircle whose radius cannot exceed $5,$ is

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Aicharya · Accepted Answer

Radius $\leq 5$ $ \begin{array}{l} \sqrt{\frac{\lambda^{2}}{4}+\frac{(1-\lambda)^{2}}{4}-5} \leq 5 \Rightarrow \lambda^{2}+(1-\lambda)^{2}-20 \leq 100 \ \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 \ \quad(	ext { approx. }) \ 	herefore \lambda=-7,-6,-5, \ldots \ldots .7,8, 	ext { in all } 16 \end{array} $values

The number of integral values of $\lambda$ for which $\mathrm{x}^{2}+\mathrm{y}^{2}+\lambda…

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