Mathematics - Circle Question with Solution | TestHub

MathematicsCircleGeneral, Basic geometries, Definition Diametrical form of circleMedium2 minPYQ_2016

MathematicsMediumsingle choice

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

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Solution:

Radius $\leq 5$ $\frac{λ ^{2}}{4} + \frac{( 1 - λ ) ^{2}}{4} - 5 \leq 5 \Rightarrow λ^{2} + (1 - λ)^{2} - 20 \leq 100 \Rightarrow 2 λ^{2} - 2 λ - 119 \leq 0 ∴ \frac{1 - 239}{2} \leq λ \leq \frac{1 + 239}{2} \Rightarrow - 7.2 \leq λ \leq 8.2 (approx.) ∴ λ = - 7, - 6, - 5, \dots\dots .7, 8, in all 16$ values

Stream:BITSATSubject:MathematicsTopic:CircleSubtopic:General, Basic geometries, Definition Diametrical form of circle

⏱ 2mℹ️ Source: PYQ_2016

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