Find The Parametric Equations

Introduction to find the parametric equation:

Parametric equation is defined as, the set of equation that has the coordinates of the variables like (x, y and z) of a curve  in terms of one or more independent variables ( parameters).

This equation below shows the general form of parametric equations.

x=x(t) and y=y(t)

Using these parametric equations, graph can be drawn for the given function. I like to share this Solving Polynomial Equations with you all through my article.


find the parametric equations - Example problems


Example : 1 Find the parametric equations for the line through the points (6,4)and (2,6) so that when t = 0 we are at the point (6,4) and when t = 1 we are at the point (2,6).

Solution:

we write symbolically,

(X, t)=(1-t)(6,4)+(t)(2,6)

= (6-6t+2t, 4-4t+6t)

=(6+4t,4+2t)

So that x(t)=6+4t and y(t)=2+4t

The final answer: x (t) =6+4t and y(t)=2+4t

Example: 2 Find the parametric equations for the line through the points (4,5)and (7,8) so that when t = 0 we are at the point (4,5) and when t = 1 we are at the point (7,8).

Solution:

We write symbolically,

(x,t)= (1-t)(4,5)+(t)(7,8)

=(4-4t+7t,5-5t+8t)

=(4+3t,5+3t)

So that x(t)=4+3t and y(t)=5+3t

The final answer: x(t)=4+3t and y(t)=5+3t

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find the parametric equations - More Example problems:


Example 3: Find the parametric equations for the line through the points (9,4)and (6,2) so that when t = 0 we are at the point (9,4) and when t = 1 we are at the point (6,2).

Solution:

Given that,

We write symbolically,

(x,t)=(1-t)(9,4)+(t)(6,2)

=(9-9t-4t,4-4t-2t)

=(9-13t,4-6t)

So that x(t)=9-13t and y(t)=4-6t

The final answer: x(t)=9-13t and y(t)=4-6t

Example 4: Find the parametric equations for the line through the points (4,1)and (2,3) so that when t = 0 we are at the point (4,1) and when t = 1 we are at the point (2,3).

Solution:

Given that,

We write symbolically,

(x,t)=(1-t)(4,1)+(t)(2,3)

=(4-4t-t,1-t-3t)

=(4-5t,1-4t)

So that x(t)=4-5t and y(t)=1-4t

The final answer: x(t)=4-5t and y(t)=1-4t

Example 5: Find the parametric equations for the line through the points (5,6)and (9,4) so that when t = 0 we are at the point (5,6) and when t = 1 we are at the point (9,4).

Solution:

Given that,

We write symbolically,

X(t)=(1-t)(5,6)+(t)(9,4)

=(5-5t-9t,6-6t-4t)

=(5-14t,6-10t)

So that x(t)=5-14t and y(t)=6-10t

The final answer: x(t)= 5-14t and y(t)=6-10t