Optimization problem I'm having trouble with

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I have this optimization problem and I am not too sure how to proceed to solve it. So there is a continent y = (x+1)^2 +1 and an island (x^2)+(y^2)=1. We want to build a bridge that links the two functions at points (x1,y1) and (a,b). Here is what the problem is asking for:

a) Formulate a question that consists of minimizing the cost, a problem without constraints of minimization of a degree 4 polynomial with 2 variable x1 and θ, so C(x1,θ) and formulate the conditions of first order.
b) Knowing that the minimum for the cost is reached for
θ=0.562371782 rad and x1=-0.68709
determine the coordinates for the points P1=(x1,y1) and P2=(a,b)

Whats the cost function. What exactly are we trying to minimize?

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Originally Posted by jakncoke

Whats the cost function. What exactly are we trying to minimize?

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They don't give me a cost function. They want me to formulate a way to minimize the cost for the construction of the bridge (so minimizing the distance between the continent and the island I guess). Also sorry if my problem is hard to understand, I am not in an English school and just tried my best to translate the problem.

I'm not really understanding, you have a function which has the point (0, 1), and (0,1) is also on the circle
They are already connected at point (0,1) ? So why do you need a bridge.

Sorry I wrote it wrong. It's y= (x+1)^2 +1