how to find the parametric equation of any curve like ellipse and hypocycloid?

Question

pls tell me the uses of differential eq. in detail within 15 minutes

Answer 1

In a space curve the parametric equation can be found like this... x=f(t), y=g(t), z=h(t), so if you have a curve defined by a vector funtion (for example): r(t)= (1+t, 2+5t, -1+6t) the parametric equation would be x=1+t, y=2+5t, z= -1+6t or for another example... r(t) = cost i + sint j + t k then the parametric equation for this curve would be x= cos t, y = sin t, z=t. This is only for curves hope this helps.

Answer 2

for ellipse:(x^2/a^2)+(y^2/b^2)=1, where a and b are parameters.


Using differential equations we can solve
1. Find solutions of wave equation.
2. solve 1D and 2D heat equations and laplace equations.