The problem is:
Find the equation of a circle given its center (2, -3) and pass through the intersection of lines x - 2y = 6 and x + 3y = 1
1. find the point of intersection of the lines (solve the simultaneous equations).
2. find the distance from the point of intersection found above to the point (2,-3), this is the radius.
3. You now have the centre and radius, so you can write down the equation.
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CB