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	Find the equation of the normal to the parabola $frac{y^{2}}{16x}=p$ at the parametric coordinates $left (frac{pt^{4}}{4}, 2pt^{2} ight )$ where p is constant. Mathematical Calculation
2	Find the equation of the tangent to ellipse $frac{x^{2}}{9}+frac{y^{2}}{4}=1$ at the parametric coordinates $(3 cos heta , 2 sin heta)$ . Mathematical Calculation
3	Derive the equations of asymptotes of a hyperbola $frac{x^{2}}{a^{2}}-frac{y^{2}}{b^{2}}=1$ Mathematical Calculation
4	Find the eccentricity and foci of the curve $frac{(x-2)^{2}}{4}-frac{(y-3)^2}{9}=1$ . Mathematical Calculation
5	Prove that the equation $r=frac{4}{1+ cos heta}$ represents a translated parabola. Mathematical Calculation
6	Given the equation $y+frac{x^{2}-10x+25}{12}-4=0$ Write the equation in the standard form of the parabola. Find the line of symmetry of the parabola in (i). Find the focus of the parabola in (i). Mathematical Calculation
7	Find the foci and the directrix of the ellipse $4x^{2}+16y^{2}=25$ . Hence, identify the major axis of the ellipse where the foci are located. Mathematical Calculation
8	Find the equation of the tangents to the curve $frac{y}{x^{2}}=frac{-1}{8}$ that will pass through the point (1,1). Mathematical Calculation
9	Show that a curve defined by the parametric equations $x=frac{2}{3}t+7$ and y=5t-1 is a straight line. Mathematical Calculation
10	If $y^{2}=16-(x-1)^{2}$ is an equation of a circle, verify whether its radius is $cos heta pm sqrt{cos ^{2} heta +15}$ where $heta$ is an angle made by the radius and the polar axis. Mathematical Calculation