Question

Solve: $144y^4-337y^2+144=0$

Answer 1

The equation of the radical axis for a pair of circles $S_1$ and $S_2$ is given by
$S_1-S_2=0$. In the above case $S_1=0\to x^2+y^2-144=0$ and $S_2=0\to x^2+y^2-15x+11y=0$.
Hence $S_1-S_2=0$ implies $-144+15x-11y=0$ or $15x-11y=144$.
Hence the equation of the radical axis is $15x-11y=144$.