How centre of projection and vanishing point are same?

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We know that in perspective projection Object positions are transformed to the view plane along lines that converge to the projection reference (center) point Which is like this:enter image description here

But many websites saying that COP(Centre of projection) and vanishing point both are same. But we know that Parallel lines that are not parallel to the viewing plane, converge to a vanishing point vanishing point. In the above picture if I draw the parallel line through the point $A, B, C$ then they are intersects at infinity which is vanishing point.

My question is how COP and vanishing point both are same?