In Exercises 1315 find two different sets of parametric equa

In Exercises 13-15, find two different sets of parametric equations for the given rec- tangular equation. (There are many correct answers.)

14. x +y^2 = 4

first part : x=t and y= sqrt(4-x) = sqrt(4-t)

Now 2nd part : x=y; Let rearrange equ: y^2= 4-x

Let 4-x = t^2--> x= 4-t^2

y = sqrt(4-x) = t

So, y=t ; x= 4-t^2

we have two sets of parameteric equation

15 ) x^2 +4y^2 -16 =0

First part : x=t ;

4y^2 = 16 -x^2

y= sqrt[(16-x^2)/4] = sqrt[(16 - t^2)/4]

y =sqrt[(16 - t^2)/4]

x=t

2nd part : Lets re-arrange the equation :

x^2 +4y^2 = 16

x^2/16 +y^2/4 =1

Let x= 4t

So, 16t^2/16 +y^2/4 =1

y^2/4 = 1-t^2

y^2 = 4(1 - t^2)

y = 2sqrt[1- t^2]

x= 4t

We have two sets of parametric equation