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# Find the radical axis of the pairs of circles ${x^2} + {y^2} - xy + 6x - 7y + 8 = 0$ and ${x^2} + {y^2} - xy - 4 = 0$ , the axes being inclined at ${120^ \circ }$

Last updated date: 15th Mar 2023
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Hint: Make use of the equation of the radical axis of a pair of circles and solve this question
Let us consider the equation of the given two circles as ${S_1}$ and ${S_2}$.

${S_1} = {x^2} + {y^2} - xy + 6x - 7y + 8 = 0$
${S_2} = {x^2} + {y^2} - xy - 4 = 0$
Now, we know that the equation of the radical axis of a pair of circles ${S_1}$ and ${S_2}$ is given by
${S_1} - {S_2} = 0$
So, on doing ${S_1} - {S_2}$ , we get
${x^2} + {y^2} - xy + 6x - 7y + 8 - ({x^2} + {y^2} - xy - 4) = 0$