(a)[3]
Find an equation for the circle $C_1$.
(b)[2]
Find an equation for the circle $C_2$.
(c)[4]
Show that the equation of line $RS$ is $y = -2x + 13$.
(d)[2]
Hence show that the $x$-coordinates of $R$ and $S$ satisfy $5x^2 - 60x + 159 = 0$.
Mathematics 9709 · AS & A Level · Coordinate geometry
Coordinate geometry — practice question
The endpoints of a diameter of circle $C_1$ are $(-3, -5)$ and $(7, 3)$. Circle $C_1$ is shifted by $\begin{pmatrix}8\\4\end{pmatrix}$ to form circle $C_2$, as the diagram shows.