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

Question 25

The quadratic $f(x)=x^2+px+q$ intersects the x-axis and y-axis at three distinct points. The circle through these points intersects the graph at a fourth point. What are its coordinates?

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