Why Does the Minimum Radius of Curvature Occur at the Apex in Parabolic Motion?

[F.Turner]

Homework Statement

A projectile in uniform gravitational field g=-g*j$$\hat{}$$ with initial location x(t=0)=$$_{}x$$o, y(0)=$$_{}y$$o show explicitly that the minimum value of radius of curvature $$\partial$$ of the resulting parabolic trajectory occurs at the apex and equal to ($$^{}v$$ox)^2/g

Homework Equations

Dynamic vector kinematics equations

The Attempt at a Solution

I have set up two equations that i believe I will need but still I'm stuck i am not to sure if the route I'm taking is correct. Would like to know what should be the initial setup for this problem.

 

[kuruman]

Start by writing an equation y(x) giving the parabolic trajectory.

 

[F.Turner]

Okay, I think I'm heading in the right direction now, I am trying to evaluate the radius of curvature as a function of position from there i will attempt to...not sure yet