Question

The radius of the circle represented by the equations,
$3x^2+3y^2+\lambda xy+9x+(\lambda -6)y+3=0$ is:

• A. $\frac{3}{2}$
• B. $\frac{\sqrt{17}}{2}$
• C. $\frac{2}{3}$
• D. $\frac{\sqrt{17}}{4}$
  

Answer 1

The correct option is A $\frac{3}{2}$

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

This equation ${ax}^2+{by}^2+2hxy+2gx+2fy+c=0$ represents circle if $a=bandh=0$

Coefficient of $xy=0$

$\Rightarrow \lambda =0$

Therefore, the equation of circle will be-

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

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

Therefore,

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

$=\sqrt{\frac{9}{4}+1-1}=\frac{3}{2}$