The points p and q define a line.

p=-1+1.875*i

q=-7.5625-(3.9375*i)

The point f is focus of the parabola.

f=-5+5*i

This is the equation of the line passing between p and q.

a*x+b*y+1=0

function('DistanceToLine',x)=abs(a*Re(x)+b*Im(x)+1)/sqrt(a^2+b^2)

function('DistanceToFocus',x)=abs(f-x)

P=x+i*y

The parabola is the locus of points P which are equidistant from both the line and the focus:

function('DistanceToLine',P)-function('DistanceToFocus',P)=0

Solve for the coefficients of the line:

a=(Im(p)-Im(q))/(Re(p)*Im(q)-(Re(q)*Im(p))),b=(Re(q)-Re(p))/(Re(p)*Im(q)-(Re(q)*Im(p)))

Graph of the formula

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