we have that
focus (-5, 3) and vertex (-5, 6)
As the vertex (−5,6) and focus (−5,3) share same abscissa −5, parabola has axis of symmetry as x=−5
Hence, equation of parabola is of the type (y−k)=a(x−h)²,
where (h,k) is vertex
Its focus then is (h,k+1/(4a))
(h,k)=(-5,6)
(h,k+1/(4a))=(-5,3)
(y−k)=a(x−h)²-----> (y−6)=a(x+5)²
k+1/(4a)=3------> 6+1/(4a)=3-----> 1/(4a)=-3-----> a=-1/12
(y−6)=a(x+5)²------> (y−6)=(-1/12)*(x+5)²
the answer is
(y−6)=(-1/12)*(x+5)²