Question

Radical axis of the circles $3x^2+3y^2-7x+8y+11=0$ and $x^2+y^2-3x-4y+5=0$ is

• A. $x+10y=2$
• B. $x+10y+2=0$
• C. $x+10y=8$
• D. $x+10y+8=0$

Answer 1

Answer: (A)

Let $S_1\equiv 3x^2+3y^2-7x+8y+11=0$
$\Rightarrow$ $S_1\equiv x^2+y^2-\frac{7}{3}x+\frac{8}{3}y+\frac{11}{3}=0$ and
$S_2\equiv x^2+y^2-3x-4y+5=0$
Radical axis, $S_1-S_2=0$
$\Rightarrow$ $\left(x^2+y^2-\frac{7}{3}x+\frac{8}{3}y+\frac{11}{3}\right)$
$-(x^2+y^2-3x-4y+5)=0$
$\Rightarrow$ $-\frac{7}{3}x+3x+\frac{8}{3}y+4y+\frac{11}{3}-5=0$
$\Rightarrow$ $\frac{2}{3}x+\frac{20}{3}y-\frac{4}{3}=0$
$\Rightarrow$ $2x+20y-4=0$
$\Rightarrow$ $x+10y-2=0$