IKMC 2018 - Grades 11-12 - Set 2 - Self-study Question 25

Question 25

The parabola $y=f(x)=x^2+px+q$ meets the two coordinate axes at three distinct points. The circle through those points meets the parabola at a fourth point. What are that point’s coordinates?

$(0,-q)$
$(p,q)$
$(-p,q)$
$(-q/p,q^2/p^2)$
$(1,p+q+1)$