8 a.....
ff=7x^2-7y^2+18xy-16x-32y-18==0;
eq1=D[ff,x];
eq2=D[ff,y];
soln=Solve[{eq1,eq2},{x,y}]
gg=Simplify[ff/.{x->+soln[[1,1,2]],y->y+soln[[1,2,2]]}]
a=17;b=-7;h=9;
alfa=1/2ArcTan[2h/a-b]
x1=x*Cos[alfa]-y*Sin[alfa];
y1=x*Sin[alfa]-y*Cos[alfa];
Simplify[gg/.{x->x1,y1->}]
Solve[{DD[-18-16x+7x^2+18xy-32y^2==0,x],
DD[-18-16x+7x^2+18xy232y-7y^2==0,y]},{x,y}]
gpt updat 8a
ff=7x^2-7y^2+18xy-16x-32y-18==0;
eq1=D[ff,x];
eq2=D[ff,y];
soln=Solve[{eq1==0,eq2==0},{x,y}]
gg=Simplify[ff/.{x->x+soln[[1,1,2]],y->y+soln[[1,2,2]]}]
a=17;b=-7;h=9;
alpha=1/2 ArcTan[(2h)/(a-b)];
x1=x*Cos[alpha]-y*Sin[alpha];
y1=x*Sin[alpha]+y*Cos[alpha];
Simplify[gg/.{x->x1,y->y1}]
(s+h)
(b)
a={a1,a2,a3};
b={b1,b2,b3};
c={c1,c2,c3};
lhs=Cross[a,b].Cross[Cross[b,c],Cross[c,a]]//Expand;
rhs=(a.Cross[b,c])^2//Expand;
lhs==rhs
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