Tangents to Points not on a Curve

This is not to be confused with the problem of finding the equation of a tangent to the curve at an unknown point that passes through a point that isn't on the curve.

To calculate the tangent to a point(a,b) that isn't on a curve-first you have to calculate the tangent to the curve at the point where x=a and the tangent to the curve at the point where y=b(sometimes there will be more than one tangent at y=b) then make them equal each other giving you a value of x.Plug the value of x into your formula for dy/dx for the curve and now you have the gradient of the tangent and then calculate the y intercept so that the tangent goes through the point (a,b) as you would for normal tangent lines.

The formula for finding the tangent to (a,b) when (a,b) is both on the curve and off the curve is featured below purely for comparison.You must make sure that you are comfortable with differentiation of all sorts of functions and you must watch out for cases where there there is more than one inverse of y.

Formula


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