A parametric curve in the plane is a pair of functions
where the two continuous functions define ordered
pairs (x,y). The two equations are usually called the parametric
equations of a curve. The extent of the curve will depend on the
range of t and your work with parametric equations should
pay close attention the range of t . In many applications,
we think of x and y "varying with time t
" or the angle of rotation that some line makes from
an initial location.
1. Let us compare what happen for the equations
You can explore with different values of a and b here. However, observe that a give us the intercept with x axis and b give us the intercept with y-axes. it looks like our initial circle were changing its form looking like an ellipse.
What is the curve when a < b? a = b? a > b?
What will happen if we combine the situation in 1 with the situation in 2? any idea?
Let us try the next combined equations
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