Circle 5 Question 13
13. The equation of the line passing through the points of intersection of the circles $3 x^{2}+3 y^{2}-2 x+12 y-9=0$ and $x^{2}+y^{2}+6 x+2 y-15=0$ is… .
(1986, 2M)
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Solution:
- Equation of straight line passing through intersection of two circles $C _1$ and $C _2$ is $\left(S _1-S _2\right)=0$.
$\therefore x^{2}+y^{2}-\frac{2}{3} x+4 y-3-\left(x^{2}+y^{2}+6 x+2 y-15\right)=0$
$\Rightarrow \quad \frac{20}{3} x-2 y-12=0 \Rightarrow 10 x-3 y-18=0$
