Tangent, Secant & Normal Lines

[nycmathguy]

Can you please provide a geometric interpretation of the tangent, secant, and normal line on the xy-plane? Please, use a different color for each line.

Thank you.

 

[MathLover1]

The normal line to a curve at a particular point is the line through that point and perpendicular to the tangent.

two special lines are the tangent line and the secant line

Tangent is a Latin word meaning to touch, and in mathematics a tangent line touches an arbitrary curve described by y=f(x) at a point P but not any other points nearby as shown.

Secant is a Latin word meaning to cut, and in mathematics a secant line cuts an arbitrary curve described by y=f(x) through two points P and Q.
The figure shows two such secant lines of the curve f to the right and to the left of the point P, respectively.

 

[nycmathguy]

The normal line to a curve at a particular point is the line through that point and perpendicular to the tangent.

two special lines are the tangent line and the secant line

Tangent is a Latin word meaning to touch, and in mathematics a tangent line touches an arbitrary curve described by y=f(x) at a point P but not any other points nearby as shown.

View attachment 2303

Secant is a Latin word meaning to cut, and in mathematics a secant line cuts an arbitrary curve described by y=f(x) through two points P and Q.
The figure shows two such secant lines of the curve f to the right and to the left of the point P, respectively.
View attachment 2302

So, Q_1 through Q_4 are secant lines. All four lines cut through point P.