Parametric Equations 

  • Created by: eleanor
  • Created on: 19-04-15 11:44
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  • Parametric Equations
    • Finding the cartesian equation
      • Rearrange 1 equation to get t=
        • then substitute into the second equation
      • use known identities to combine the 2 equations
        • rearrange to get sint or cos(t)
          • substitue into an equation linking both sin and cos
    • finding where the curve crosses the axes
      • x-axis- y = 0 so set the parametric equation for y equal to 0 and slove for t
        • then substitute t into the equation for x to find the point
    • finding the value of t at a particular point
      • if you have a point a,b  then set x(t) = a and y(t)= b and solve to find t
    • finding where a parametric curve crosses a straight line
      • find the coordinates of the points of interesection of the curve
        • substitute the parametric equation into the line
          • solve to find t
            • substitute t back into the parametric equation
    • Differentiation
      • as we have an extra variable t we must use the chain rule
        • dy/dx= dy/dt x dt/dx
        • remember to flip dx/dt to get dy/dx
    • Integration
      • in order to include t the formula is y(dx/dt) dt
        • integrate with resoect to t
        • differentiate the x-part
      • find dx/dt
        • rewrite the integral in terms of t
          • change the limits into terms of t
            • then solve


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