Can the intersection points between a circle and a parabola be algebraicly defined? I end up with polynomial degree 6. Thank you.
2 visualizzazioni (ultimi 30 giorni)
Mostra commenti meno recenti
Karl
il 29 Mag 2023
Risposto: Shaik mohammed ghouse basha
il 29 Mag 2023
Circle equation:(x-m)^2+(y-n)^2=r^2 Parabola equation: (x-h)^2=4*f*(y-k)
0 Commenti
Risposta accettata
Shaik mohammed ghouse basha
il 29 Mag 2023
Hello,
As for my interpreation of your question, you are asking for a generalised equation for x and y coordinates when a circle of equation intersects with parabola of equation
The point of intersection lies on both circle and parabola. Let the point be of form (h+t, k + (t^2/4f) ).
This point lies on circle so we can write,
Upon expanding this equation you get a polynomial of degree 4.
Solving these equation you get possible values of t.
Using these value you can find the intersection points by inserting values of t in
This approach reduces polynomial to be solved from 6 degree to 4 degree but general terms can be quite complex.
For a four degree equation of form
we have solutions:
You can find a general equation by solving that four degree polynomial and substituing in coordinates but they turn out to be very complex.
0 Commenti
Più risposte (0)
Vedere anche
Categorie
Scopri di più su Polynomials in Help Center e File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!