2026 NYGH P1 Q7

During the recent school funfair, Class 413 manned a dart game at their class booth. Players had to throw darts and hit the target to win a prize. The dart target consists of two concentric circles, an outer circle \(C_1\) and an inner circle \(C_2\). The equation of \(C_1\) is \(x^2+y^2-6x+10y-47=0\).

1. Given that point \((7,-5)\) lies on \(C_2\), determine the equation of \(C_2\).[4]
2. A dart is thrown and lands at point \(P(4,-10)\). Explain, with clear working, whether the dart lands in the inner circle, in the region between the inner and outer circles, or outside the target entirely.[2]