Question

If $2x^2+\lambda xy+2y^2+(\lambda -4)x+6y-5=0$ represents a circle, then its radius is

• A. $2\sqrt{2}$
• B. $3\sqrt{2}$
• C. $\frac{\sqrt{23}}{2}$
• D. $Noneofthese$

Answer 1

The correct option is C $\frac{\sqrt{23}}{2}$

Given,

$2x^2+\lambda xy+2y^2+(\lambda -4)x+6y-5=0$

$\Rightarrow x^2+\frac{\lambda xy}{2}+y^2+\frac{(\lambda -4)}{2}x+3y-\frac{5}{2}=0$...(1)

General equation of circle $x^2+y^2+2gx+2fy+c=0$...(2)

Comparing (1) and (2), we get,

$\lambda =0$

$r=\sqrt{g^2+f^2-c}$

$=\sqrt{(-1{)}^2+{\left(\frac{3}{2}\right)}^2+\left(\frac{5}{2}\right)}$

$\therefore r=\frac{\sqrt{23}}{2}$