Question

The equation ${\lambda }^2{x}^2+({\lambda }^2-5\lambda +4)xy+(3\lambda -2)y^2-8x+12y-4=0$ will represent a circle , if $\lambda =$

• A. $1$
• B. $4$
• C. $2$
• D. $3$

Answer 1

The correct option is A $1$

For any two degree

An equation to be an

Equation of circle

$a{x}^2+b{y}^2+2hxy+2gx+2fy+c=0$

$a=b,h=0$

comparing

${\lambda }^2=3\lambda -2$ ${\lambda }^2-5\lambda +4=0$

$\lambda =1,2$ $\lambda =1,4$

So common value of $\lambda =1$