Page 301 - DMTH201_Basic Mathematics-1

Basic Mathematics – I

Notes

11.4 Parametric Functions

If the variables x and y are given in terms of a new variable t, then the function is said to be in the
parametric form and ‘t’ is called the parameter.
In general, the parametric function is given by x f t ,y g t where f t and g t are
functions of the parameter t.
x f t ,y g t are called the parametric equations.

dy
To find when the parametric equations are given
dx

Let x f t and y g t be the parametric equations.

dx
Differentiate x f t w.r.t. t to get
dt
dy
Differentiate y g t w.r.t. t to get
dt
dy
dy dt
then
dx dx
dt
This method of differentiation is called Parametric Differentiation.

dy
Example: Find , if, x at 2 ,y 2at
dx
Solution:
Differentiating both the equations w.r.t. t, we get

dx dy
2 at, 2 a
dt dt
dy dy /dt 2a 1
dx dx /dt 2at t

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