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Plot a curve in the region defined

I have the following region :

p, t= var('p t') 
c=(p*t^2-p^2*t)+(t^2+2*t*p+p^2)+t-p #3 sides (a,b,c) in terms of theta and phi
region_plot([a+b>=c, b+c>=a, c+a>=b], (t,-2,2), (p,-2,2))

And I want to plot a curve C=t*p*(t-p)+t*p+2*(t-p)-1 on the region in first quadrant. How am I suppose to do that.