# Parametric Equations

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• Created by: eleanor
• Created on: 19-04-15 11:44
• 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