First slide

Definition of a circle

Question

if $2 (x^{2} + y^{2}) + 4 λ x + λ^{2} = 0$ represents a circle of
meaningful radius, then the range of real values of $λ$ ., is

Moderate

A

$R$
B

$(0, \infty)$
C

$(- \infty, 0)$
D

none of these

Solution

We have
$2 (x^{2} + y^{2}) + 4 λ x + λ^{2} = 0 \Rightarrow x^{2} + y^{2} + 2 λ x + \frac{λ^{2}}{2} = 0$
This equation will represent a circle of meaningful radius if
$λ^{2} + 0 - \frac{λ^{2}}{2} \geq 0 \Rightarrow \frac{λ^{2}}{2} \geq 0$ which is true for all $λ \in R$

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