The equation of radical axis of the circles x 2 + y 2 + 4 x + 6 y + 7 = 0 and 4 x 2 + 4 y 2 + 8 x + 12 &#160…

Given: $S_1: x^2+y^2+4x+6y+7=0$

$S_2: 4x^2+4y^2+8x+12y-9=0$

Equation of radical axis of circles is $S_1-S_2=0$

$S_1: x^2+y^2+4x+6y+7=0$

$S_2: x^2+y^2+2x+3y-\frac{9}{4}=0$

Radical axis:

$S_1-S_2=0$

$\Rightarrow \left(x^2+y^2+4x+6y+7\right)-\left(x^2+y^2+2x+3y-\frac{9}{4}\right)=0$

$\Rightarrow 2x+3y+\frac{37}{4}=0$

$\Rightarrow 8x+12y+37=0$