Question

If ax $+$ by $+ca=0$, where a,b,c>0 is the equation of the common radical axis of the coaxial system $(3x^2+3y^2-2x-2y-1)+\lambda (x^2+y^2-x-2y-3)=0$ , then $ab+bc+$ ca $=$

• A. $44$
• B. $13$
• C. $40$
• D. $12$

Answer 1

The correct option is A $44$

Equation of radical axis is $s_1-s_2=0$.
Put $\lambda =0$. $s_1=x^2+y^2-\frac{2x}{3}-\frac{2y}{3}-\frac{1}{3}=0$
and $s_2:x^2+{\lambda }^2-x-2y-3=0$
$\therefore s_1-s_2=0$
$\frac{x}{3}+\frac{4y}{3}+\frac{8}{3}=0$
$x+4y+8=0$
$ax+by+c=0$
$a=1,b=4$ & $c=8$
$\therefore ab+bc+ac=4+32+8$
$=44$