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by

:

then the slope of the tangent is

:

giving the equation for the tangent line at as

:

If

:

the tangent line is not defined. However, it may occur that the tangent line exists and may be computed from an implicit equation of the curve.

Normal line to a curve

The line perpendicular to the tangent line to a curve at the point of tangency is called the normal line to the curve at that point. The slopes of perpendicular lines have product -1, so if the equation

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