Question

can someone explain or site some examples regarding with PARAMETRIC EQUATIONS?

Answer 1

The normal way we think about things with equations is that y is dependent on x. so we give and x and we get a y. but it would sometimes be nice to be able to talk about y independently of x. so imagine being able to identify the y's without knowing the x. we do this by making a "third axis" call it t. so x depends on t and y depends on t. no longer does y depend on x. now the hard part is coming up with those equations. here is an easy example.
y = x^2
right now y depends on x. but now if we say, y = t^2 and x = t, then we no longer need to depend on x for our values. This case is a very simple case and seems to trival so we can consider a little bit harder case.
\[1=x^2+y^2\]
this is of course the equation of a circle centered at the origin with radius 1
we know this is a circle and right now the y depends on x, but if we say
x=cos(t) and y=sin(t)
this is also a circle at the origin with radius 1.
t is our input.

Answer 2

note also we are working with equations and not functions so we can think about y depending on x or x depending on y, but either way when we parametrize we no longer have them depending on each other.

Answer 3

question? I need to go to sleep.

Answer 4

maybe after digesting this all. thank you so much :))

Answer 5

np