How can I make a program that accepts equations then prints out if "CIRCLE", "ELLIPSE", "PARABOLA" or "HYPERBOLA". This is my first try. The problem is that!!! It won't work. I think this is my 3rd work.

When I enter x^2+y^2 it says ELLIPSE. Its supposed to be a CIRCLE

If x² and y² both have the same coefficients like x² + y² or 3x² + 3y², then it is a circle.

If x² and y² both have different coefficients that have the same sign, like 4x² + 9y², or x² + 16y², then it is an ellipse.

If x² and y² have different signs, like 25x² - 9y², or 16y² - x², then it is a hyperbola.

If the equation has either x² and y², but not both, then it is a parabola.I'm also thinking that my way is not the best way because it uses TOO much conditions. I think...Code:#include <ctype.h>#include <stdbool.h> #include <stdio.h> #include <stdlib.h> #include <string.h> int main(void) { char eq[256]; bool x_exist = false, y_exist = false, neg_exist = false; int x, y; fgets(eq, 256, stdin); for (int i = 0, end = strlen(eq); i < end; i++) { if (eq[i] == 'x') { x_exist == true; if (eq[i - 1] == '-' && neg_exist == false) { x = 1; neg_exist = true; } else if (eq[i - 1] == '+') x = 1; else if (isdigit(eq[i - 1])) { x = atoi(&eq[i - 1]); if (eq[i - 1] == '-' && neg_exist == false) { x = 1; neg_exist = true; } else if (eq[i - 1] == '+') x = 1; } } else if (eq[i] == 'y') { y_exist == true; if (eq[i - 1] == '-' && neg_exist == false) { y = 1; neg_exist = true; } else if (eq[i - 1] == '+') y = 1; else if (isdigit(eq[i - 1])) { y = atoi(&eq[i - 1]); if (eq[i - 1] == '-' && neg_exist == false) { y = 1; neg_exist = true; } else if (eq[i - 1] == '+') y = 1; } } } if ((!y_exist && x_exist) || (y_exist && !x_exist)) printf("PARABOLA"); else if (x == y) printf("CIRCLE"); else if (x != y) printf("ELLIPSE"); else if (neg_exist) printf("HYPERBOLA"); return 0; }