Question

The radius of the circle representd by the equation $3x^2+3y^2+\lambda xy+9x+(\lambda -6)y+3=0$

• A. $\frac{3}{2}$
• B. $\frac{\sqrt{17}}{2}$
• C. $\frac{2}{3}$
• D. None of these

Answer 1

The correct option is A

$\frac{3}{2}$

The equation of the circle is $3x^2+3y^2+\lambda xy+9x+(\lambda -6)y+3=0$

$\therefore$ Coefficient of xy=0

$\Rightarrow \lambda =0$

$\therefore 3x^2+3y^2+9x-6y+3=0$

$\Rightarrow x^2+y^2+3x-2y+1=0$

Therefore, the radius of the circle is

$\sqrt{{\left(\frac{3}{2}\right)}^2+(-1{)}^2-1}=\frac{3}{2}$