[ML Question] Error of a linear regression line

We are given a one dimensional data. The value of the single feature lies in the closed interval \([-2, 2]\). The associated target value corresponding to each data point, lies in the closed interval \([-2, 2]\), such that if we plot the feature value on x-axis and the associated target value on y-axis, then we get a circle.

Assume that we fit a linear regression line to the data, we can get infinite regression lines passing through origin. Can we derive the formula for error? Will the error be same for every regression line passing through origin?