MATLAB: Solving 5 non linear simultaneous equation

Question

I have a set of 5 non-linear equations. first 4 equations are h,k,a,b –> in terms of variable 'bsfc'. the fifth equation bsfc^2 in terms of h,k,a,b. So i have 5 equations and 5 variables. This programming is basically finding the radius of the rotated ellipse. I have my x and y values too. However I am not getting the right solution.

The right solution is bsfc=246

I have my code here:

syms bsfc h k a b
   y=86;
   x=1717;
   phi=0;
   eqn1= h == 9.514*bsfc;
   eqn2= k == 0.0001*(bsfc+1)^2-0.07*bsfc+19;
   eqn3= a == 10* atan(bsfc/30 - 5.8) -3.5;
   eqn4= b == 0.025 * atan(bsfc/20 - 10.3) -0.022;
   eqn5= bsfc^2 == (((x-h)*cos(phi)+(y-k)*sin(phi))^2/(a^2)+ ((x-h)*sin(phi)-(y-k)*cos(phi))^2/(b^2))
sol=solve([eqn1,eqn2,eqn3,eqn4,eqn5],bsfc,h,k,a,b);
hSol = sol.h
kSol = sol.k
aSol = sol.a
bSol = sol.b
bsfcSol = sol.bsfc

Answer 1

Given those equations, bsfc approximately 1154.643046927194 or approximately 1325.553297436922

Your proposed value 246 does not come at all close to satisfying eqn5