Orbital speed of an object in a circular orbit

[Natchanon]

Homework Statement

Consider a central force is attractive but which passes through the force center. In other words, consider an orbit of radius a which is centered at (a,0), with the force center at the origin
c.) Suppose the speed at the apogee is v₀ Find the oribital speed v as a function of angle B, defined as the angle from the x-axis swept by a radial line from the center of the orbit (not the origin)

Homework Equations

L = mvr

The Attempt at a Solution

I let L at apogee equal l at any point. So, m v_0 2a = m v(B) r, where I use law of cosines to write r in term of B. and V(B) = 2*V_0 / sqrt( 2*(1-cos(pi - B) ). But I'm not sure if this is correct because v and r are perpendicular at apogee, but not at other points.

 

[BvU]

You need some more relevant equations to deal with this. Writing down equations for $\ddot x$ and $\ddot y$ is a start