Step 1

The focus of the parabola is given as (-1,4.5)

The vertex of the parabola is given as (-1,3)

The axis of the parabola is given as,

x=-1

Hence, the given parabola is vertical parabola,

Step 2

If the axis of the parabola is parallel to y-axis and the vertex of the parabola is (h,k) then the general equation of the parabola is given as,

\((x-h)^{2}=4a(y-k)\)

a=4.5-3

=-1.5

Putting the values, we get

\((x-(-1))^{2}=4*(1.5)(y-3)\)

\((x+1)^{2}=6(y-3)\)

\(x^{2}+1+2x=6y-18\)

\(x^{2}+2x-6y+19=0\)

Therefore, the required equation of the parabola is \(x^{2}+2x-6y+19=0\)