How to solve this equations for alfa and beta ?

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TARIK YAMAN
TARIK YAMAN 2020-8-31
clc;
clear;
syms r alfa beta x0 y0 z0 x1 y1 z1
dist(alfa,beta) = norm(([x0 - r*(sin(alfa))*(cos(beta)),y0 - r*(sin(alfa))*(sin(beta)),z0 - r*(cos(alfa))] - [x1,y1,z1]));
D(alfa,beta) = diff(dist,alfa,2)*diff(dist,beta,2) - (diff(diff(dist,alfa),beta))^2;
[ALFA_MAX,BETA_MAX] = solve(D > 0, dist(alfa,beta) < 0,alfa,beta);
[ALFA_MIN,BETA_MIN] = solve(D > 0, dist(alfa,beta) > 0,alfa,beta);
[ALFA_SAD,BETA_SAD] = solve(D < 0,alfa,beta);
[ALFA_NAN,BETA_NAN] = solve(D == 0,alfa,beta);
Hi, I want solve distance equation of between any points and any point on sphere for alfa and beta. I have get distance equation and apply second derivation test but i can not any solution.
(x1,y1,z1) : coordinates of any points.
(x0,y0,z0) : center point of sphere.
alfa : angle between z axis or parallel line passes through (x0,y0,z0) and radius.
beta : angle between radius and xy-plane.
r : radius.

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