Quadratic Formulas with Time?

[metacogitans]

How would one use a quadratic formula with time as a variable? For example, what the intersections between two circular functions would be when T=0 compared to T=5 if the radius of the functions increases over time? 

Also, is there a general equivalent of the quadratic formula for circles?

I would like to basically have a simple equation that gives me the coordinates of an intersection (x, y, z) for a given value of x, y, and time. 

After that, the derivative of an intersecting function is going to be treated as an axis for a change in slope of the other function over time (the slope will 'reverse' over the perpendicular line to the other function's derivative at the point of intersection).

The equations would be for wave equations when interactions between infinitesimally thin waves are involved.

Right now I have written the equations for this type of wave interaction, but only if I can make up a value for the other function's origin for every single intersection I am evaluating. I can't yet use them to determine what each secessive point of intersection will be without having to change the radius and origin of one of the functions for each intersection I calculate.

I am not sure if the term would be 'implicit', but with circular and spheroid functions I think what I am looking for would be called a "Implicit Quadratic Formula", as they involve variables paired with a constant together as a square root, which of course don't have a simple algebraic way of being determined. Rediscovering a proof for those types of intersections would take me weeks/months/years, and I have already tried and failed numerous times. 

With graphing algorithms, I could approximate the change in intersections over time to  a certain number of decimal places accurately through repeatedly estimating factors and adjusting them based on the range of difference, but this is labor intensive even for a computer. It'd be a lot easier if there was a more general formula like the Quadratic formula; does anyone know if it exists?

I couldn't just find the intersection between one function and the line equation perpendicular to the other's derivative, because this does not tell me what the first point of intersection would be for that perpindicular - there must be an equal increase in each function's radius over time.

Edited March 31, 2018 by metacogitans

[mathematic]

I will try to answer your first question with a general observation.  When doing mathematics,the names of the variables (time, distance, etc.) don't matter.  For your first question t is a variable to be treated like any other.

[studiot]

55 minutes ago, mathematic said:

I will try to answer your first question with a general observation.  When doing mathematics,the names of the variables (time, distance, etc.) don't matter.  For your first question t is a variable to be treated like any other.

 I wish I wish I wish I could impress this on Physicists.  +1

[metacogitans]

2 hours ago, mathematic said:

I will try to answer your first question with a general observation.  When doing mathematics,the names of the variables (time, distance, etc.) don't matter.  For your first question t is a variable to be treated like any other.

Right that works just fine for Quadratic equations but what about an equation for two semi-circles when the radius is increasing over time? I guess I'm not sure if it would still be called a quadratic formula, but what I'm looking for is a formula that gives intersection coordinates.

[MaximThibodeau]

did you try with a computer algo., with going too large value and after making it smaller until it fit? because analytic function...

[swansont]

15 hours ago, metacogitans said:

How would one use a quadratic formula with time as a variable?   

Like this?

s = vt + 1/2 at^2

22 minutes ago, metacogitans said:

Right that works just fine for Quadratic equations but what about an equation for two semi-circles when the radius is increasing over time? I guess I'm not sure if it would still be called a quadratic formula, but what I'm looking for is a formula that gives intersection coordinates.

You would solve the two equations simultaneously 

[Eric LeClair]

On 3/31/2018 at 2:01 PM, mathematic said:

I will try to answer your first question with a general observation.  When doing mathematics, the names of the variables (time, distance, etc.) don't matter.  For your first question t is a variable to be treated like any other.

100% correct but general observations can be tricky . . . Especially where fact based judgements are a necessity (Like Math / Science etc).