9709 P12 - Mar 2020 - Q12 - 11 marks
10539
A diameter of circle \(C_1\) has endpoints \((-3,-5)\) and \((7,3)\).
(a) Find its equation. [3]
\(C_1\) is translated by \(\begin{pmatrix}8\\4\end{pmatrix}\) to give \(C_2\).
(b) Find the equation of \(C_2\). [2]
The circles intersect at \(R,S\).
(c) Show that \(RS\) is \(y=-2x+13\). [4]
(d) Hence show that their \(x\)-coordinates satisfy \(5x^2-60x+159=0\). [2]
