Mathematics Pure WMA11: Coordinate geometry in the (x, y) plane Topical Past Paper Questions

The circle $C_{1}$ has equation $$ x^{2}+y^{2}-6x+5y-41=0 $$ (a) Find (i) the coordinates of the centre of $C_{1}$ (ii) the radius of $C_{1}$ The circle $C_{2}$ has (3) • centre $(-k,0)$ where $k$ is a positive constant • radius 5 Given that circles $C_{1}$ and $C_{2}$ touch (b)…

The line joining the points $ (-2, 5) $ and $ (4, 15) $ is the diameter of a circle C. (a) Find an equation for C. (b) Hence find the exact coordinates of the point on C that is nearest the x-axis. (5)

Figure 2 Figure 2 shows a sketch of the curve defined by the parametric equations $$ x=t^{2}+2t\quad y=\frac{2}{t(3-t)}\quad a\leqslant t\leqslant b $$ where $a$ and $b$ are constants. The ends of the curve lie on the line with equation y = 1 (a) Find the value of a and the value…