First slide

Definition of a circle

Question

If $3 x^{2} + 2 λ x y + 3 y^{2} + (6 - λ) x + (2 λ - 6) y - 21 = 0$ is the equation of a circle, then its radius is

Moderate

A

1
B

3
C

$2 \sqrt{2}$
D

none of these

Solution

We have,
$3 x^{2} + 2 λ x y + 3 y^{2} + (6 - λ) x + (2 λ - 6) y - 21 = 0 \dots (i)$
This equation will represent a circle, if
Coeff. of $x y = 0 \Rightarrow λ = 0$
Putting $λ = 0$ in (i), we obtain $x^{2} + y^{2} + 2 x - 2 y - 7 = 0$
Clearly, it represents a circle of radius $= \sqrt{1 + 1 + 7} = 3 .$

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