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 perpendicular distance of a point (10,10) from the tangent to the curve $4x^{2}+9y^{2}=25$ at (-18,1). Mathematical Calculation
2	Show that the equation $16x^{2}+25y^{2}-64x+150y-111=0$ is an equation of ellipse. Mathematical Calculation
3	Show that $y=mx+c$ is a tangent to the hyperbola $frac{x^2}{a^{2}}-frac{y^{2}}{b^{2}}=1$ when $c^{2}=a^{2}m^{2}-b^{2}$ . Determine the equation of a tangent line to hyperbola $5x^{2}-4y^{2}=1$ if the slope of the tangent line is -2. Mathematical Calculation
4	Transform the equation $x^{2}+y^{2}+4x=2sqrt{x^{2}+y^{2}}$ into a polar equation. Draw the graph of the polar equation obtained in (i) above in the interval $0leq heta leq2pi$ Mathematical Calculation
5	Show that the point B(5,-5) lies on the parabola $y^{2}=5x$ and find the equation of the normal to the parabola at the point B in the form y=mx+c. Mathematical Calculation
6	If y=mx+c is a tangent to the ellipse $frac{x^{2}}{a^{2}}+frac{y^{2}}{b^{2}}=1$ , find c in terms of a,b,m. Mathematical Calculation
7	Find the rectangular equation of $r=12(1+sin heta)$ . Sketch the graph of $r=sin 2 heta$ for $0leq heta leq pi$ . Mathematical Calculation
8	The ellipse has its foci at the points (-1,0) and (7,0) when its ecentricity is ½. 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
9	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
10	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