Question

The radius of the circle represented by the equation
3x² + 3y² + λxy + 9x + (λ − 6) y + 3 = 0 is
(a) $\frac{3}{2}$

(b) $\frac{\sqrt{17}}{2}$

(c) 2/3

(d) none of these

Answer 1

(a) $\frac{3}{2}$

The equation of the circle is 3x² + 3y² + λxy + 9x + (λ − 6) y + 3 = 0.
∴ Coefficient of xy = 0

$\Rightarrow \lambda =0$

$$\begin{gathered} \therefore 3x^2+3y^2+9x-6y+3=0 \\ \Rightarrow x^2+y^2+3x-2y+1=0 \end{gathered}$$

Therefore, the radius of the circle is $\sqrt{{\left(\frac{3}{2}\right)}^2+{\left(-1\right)}^2-1}=\frac{3}{2}$.