Coordinate geometry 2 questions | form six Pure Advanced Mathematics

(6641) Question Category: Mathematical Calculation

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.

Answer / Solution

UNSOLVED

(6642) Question Category: Mathematical Calculation

  1. Find the rectangular equation of r=12(1+sin heta).
  2. Sketch the graph of r=sin 2 heta for 0leq heta leq pi.

Answer / Solution

UNSOLVED

(6643) Question Category: Mathematical Calculation

  1. The ellipse has its foci at the points (-1,0) and (7,0) when its ecentricity is ½. Find its Cartesian equation.
  2. Convert y^{2}=4a(a-x) into polar equation.
  3. Use the equation y=2x^{2}-6x+4 to determine its directrix and the focus.

Answer / Solution

UNSOLVED

(6644) Question Category: Mathematical Calculation

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.

Answer / Solution

UNSOLVED

(6645) Question Category: Mathematical Calculation

  1. Define the term hyperbola
  2. 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}

Answer / Solution

UNSOLVED

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