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How do we define tangent line to curve accurately ?

I cannot say it is a straight line who intersect the curve in one point because if we draw y = x^2 & make any vertical line, it will intersect the curve and still not the tangent we know. Moreover, tangent line may intersect the curve at other points other than the tangency point.

What is the precise definition for the tangent line?

I cannot say it is a straight line who intersect the curve in one point because if we draw y = x^2 & make any vertical line, it will intersect the curve and still not the tangent we know. Moreover, tangent line may intersect the curve at other points other than the tangency point.

What is the precise definition for the tangent line?