Function Repository Resource:

TangentAndNormalLine

Compute properties of the tangent and normal lines to a curve at a given point

Contributed by: Wolfram|Alpha Math Team

ResourceFunction["TangentAndNormalLine"][expr,{x,a},{y,b}]

gives an association of properties of the tangent and normal lines to expr, viewed as an equation in x and y, at the point {x,y}={a,b}.

ResourceFunction["TangentAndNormalLine"][expr,{x,a},{y,b},prop]

returns the value of the tangent and normal lines property prop.

ResourceFunction["TangentAndNormalLine"][expr,{x,a},y]

returns information relating to one pair, among possibly several, of the tangent and normal lines to expr at x=a.

ResourceFunction["TangentAndNormalLine"][expr,x,{y,b}]

returns information relating to one pair, among possibly several, of the tangent and normal lines to expr at y=b.

Details

Allowed values of prop are:

"SlopeInterceptEquation"

equation of the tangent line in slope intercept form

"StandardFormEquation"

equation of the tangent line in standard form

"PointSlopeEquation"

equation of the tangent line in point slope form

"HorizontalIntercept"

horizontal intercept for the tangent line equation

"VerticalIntercept"

vertical intercept for the tangent line equation

"Plot"

plot of the tangent line equation

All

association of information returning all allowed properties

If expr does not have head Equal, then expr is treated as an expression defining y in terms of x. In other words, ResourceFunction["TangentAndNormalLine"][expr,{x,a},y,…] is equivalent to ResourceFunction["TangentAndNormalLine"][y==expr,{x,a},y,…] if expr has a head other than Equal.

If only one coordinate of the intersection point is given, the other coordinate is inferred. For expressions that are multivalued at the given value of x or y, information on only one of potentially several tangent and normal line pairs is returned.