Definition of a circle

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Question

The number of integral values of $λ$ for which the
equation $x^{2} + y^{2} - 2 λ x + 2 λ y + 14 = 0$ represents a
circle whose radius cannot exceed $6$ , is

Moderate

Solution

We have,
Radius $\leq 6$
$\begin{array}{ll} \Rightarrow (Radius)^{2} \leq 36 \\ \Rightarrow λ^{2} + λ^{2} - 14 \leq 36 \\ \Rightarrow λ^{2} - 25 \leq 0 \\ \Rightarrow - 5 \leq λ \leq 5 \Rightarrow λ = 0, \pm 1, \pm 2, \pm 3, \pm 4, \pm 5 \end{array}$
Hence, there are $11$ integral values of $λ$ .

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Definition of a circle

Remember concepts with our Masterclasses.

The number of integral values of λ for which the equation x2+y2−2λx+2λy+14=0 represents a circle whose radius cannot exceed 6, is

We have,Radius ≤6⇒ ( Radius )2≤36⇒ λ2+λ2−14≤36⇒ λ2−25≤0⇒ −5≤λ≤5⇒λ=0,±1,±2,±3,±4,±5Hence, there are 11 integral values of λ.

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The number of integral values of $λ$ for which the
equation $x^{2} + y^{2} - 2 λ x + 2 λ y + 14 = 0$ represents a
circle whose radius cannot exceed $6$ , is