Mathematics 7356: Coordinate Geometry in the (x,y) plane Topical Past Paper Questions

Line L has equation $$ 5y=4x+6 $$ Find the gradient of a line parallel to line L Circle your answer. $$ \begin{array}{r l r}{\mathrm{[1~m a r k]}}&{}&\\ {\mathrm{-\frac{5}{4}}}&{}&{\mathrm{-\frac{4}{5}}}\end{array}\quad\mathrm{\frac{4}{5}}\quad\mathrm{\frac{5}{4}} $$

The line $L_{1}$ has equation $x + 7y - 41 = 0$ $ L_{1} $ is a tangent to the circle C at the point $ P(6,5) $ The line $L_{2}$ has equation $y = x + 3$ $ L_{2} $ is a tangent to the circle C at the point Q(0, 3) The lines $L_{1}$ and $L_{2}$ and the circle C are shown in the dia…

AB is a diameter of a circle where A is (1, 4) and B is (7, -2) (b) Find the coordinates of the midpoint of AB. [1 mark] Show that the equation of the circle may be written as $$ x^{2}+y^{2}-8x-2y=1 $$ $ x^2 + y^2 - 8x - 2y = 1 $ [4 marks] (c) The circle has centre C and crosses…