Coordinate geometry 2 questions | form six Pure Advanced Mathematics

Find Coordinate geometry 2 examination questions, form six Pure Advanced Mathematics in acaproso.com

#	Question
1	The ellipse has its foci at the points (-1,0) and (7,0) when its ecentricity is $frac{1}{2}$ . Find its cartesian equation. Convert $y^{2}=4a(a-x)$ into polar equation. Use the equation $y=2x^{2}-6x+4$ to determine its directrix and the focus. Mathematical Calculation
2	A cable used to support a swinging bridge approximates the shape of a parabola. Determine the equation of a parabola if the length of the bridge is 100m and the vertical distance from where the cable is attached to the bridge to the lowest point of the cable is 20m. Mathematical Calculation
3	Define the term hyperbola Show that the latus rectum of the equation $frac{(x-h)^{2}}{a^{2}}-frac{(y-k)^{2}}{b^{2}}=1$ is $frac{2b^{2}}{a}$ Mathematical Calculation
4	(i) Mention any two properties of $f(x)=b^{x}$ (ii) Draw the graph of $f(x)=left ( frac{1}{2} ight ) for -3leq xleq 3$ . Mathematical Calculation
5	Given that $y=frac{x^{2}-2x-3}{x^{2}-4}$ (i)Find the vertical and horizontal asymptotes. (ii) Sketch the graph of y. Mathematical Calculation
6	Find the equation of a tangent to the ellipse 4x²+y²=6 at $(frac{1}{2}, sqrt{5})$ in the form ax+by+c=0. Mathematical Calculation
7	The points $P(at_{1}^{2},2at_{1})$ and $Q(at_{2}^{2},2at_{2})$ lie on the parabola $y^{2}=4ax$ . The tangents at the points P and Q intersect at R. Find the coordinates of R. Mathematical Calculation
8	Convert the following polar equations into Cartesian equations: $r^{2}=4sin2 heta$ $r=3(1+cos heta)$ Mathematical Calculation
9	A curve is defined by the parametric equations $x=t^{2}$ and $y=frac{2}{t}$ where $t eq 0$ . Show that the equation of the normal at the point $Qleft ( p^{2} ,frac{2}{p^{2}} ight )$ is $p^{4}x-py+2=p^{6}$ . Mathematical Calculation
10	Show that the equation of a tangent to parabola $y^{2}=4ax$ at point $(x_{1},y_{1})$ is $yy_{1}=2a(x+x_{1})$ . Mathematical Calculation